{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "569d620b-882a-4d90-a82a-e0c2bb85de9d",
   "metadata": {},
   "source": [
    "\n",
    "姚端正、周国全、贾俊基《数学物理方法》第四版P.275\n",
    "\n",
    "里兹法重解例题3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e9220533-845d-4da3-88cf-4e204859b2e2",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import *  # 导入sympy 包中所有的函数\n",
    "from sympy.abc import x # 引入默认的符号变量\n",
    "c0,c1,c2,lamd = symbols('c0 c1 c2 lambda') # 自定义符号变量"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "b1db7b4c-a630-474c-8c8a-0e2f2e33cc43",
   "metadata": {},
   "outputs": [],
   "source": [
    "y = x*(x-1)*(c0+c1*x+c2*x**2) # 增加项数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "81a5c4fa-ff42-41c2-ba96-ca44ec677482",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{c_{0}^{2}}{3} + \\frac{c_{0} c_{1}}{3} + \\frac{c_{0} c_{2}}{5} + \\frac{2 c_{1}^{2}}{15} + \\frac{c_{1} c_{2}}{5} + \\frac{3 c_{2}^{2}}{35} - \\lambda \\left(\\frac{c_{0}^{2}}{30} + \\frac{c_{0} c_{1}}{30} + \\frac{2 c_{0} c_{2}}{105} + \\frac{c_{1}^{2}}{105} + \\frac{c_{1} c_{2}}{84} + \\frac{c_{2}^{2}}{252}\\right)$"
      ],
      "text/plain": [
       "c0**2/3 + c0*c1/3 + c0*c2/5 + 2*c1**2/15 + c1*c2/5 + 3*c2**2/35 - lambda*(c0**2/30 + c0*c1/30 + 2*c0*c2/105 + c1**2/105 + c1*c2/84 + c2**2/252)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Phi  = integrate(diff(y,x)**2,(x, 0, 1)) - lamd* integrate(y**2,(x, 0, 1))\n",
    "Phi "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "25edbd4e-f5cc-4198-9adc-727b92971e53",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{2 c_{0}}{3} + \\frac{c_{1}}{3} + \\frac{c_{2}}{5} - \\lambda \\left(\\frac{c_{0}}{15} + \\frac{c_{1}}{30} + \\frac{2 c_{2}}{105}\\right)$"
      ],
      "text/plain": [
       "2*c0/3 + c1/3 + c2/5 - lambda*(c0/15 + c1/30 + 2*c2/105)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq0= diff(Phi,c0)\n",
    "eq0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "69f46e53-7489-42ea-988c-46b5bed6d127",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{c_{0}}{3} + \\frac{4 c_{1}}{15} + \\frac{c_{2}}{5} - \\lambda \\left(\\frac{c_{0}}{30} + \\frac{2 c_{1}}{105} + \\frac{c_{2}}{84}\\right)$"
      ],
      "text/plain": [
       "c0/3 + 4*c1/15 + c2/5 - lambda*(c0/30 + 2*c1/105 + c2/84)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq1= diff(Phi,c1)\n",
    "eq1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "f61235f5-dcbc-4e77-a3d9-80665c175883",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{c_{0}}{5} + \\frac{c_{1}}{5} + \\frac{6 c_{2}}{35} - \\lambda \\left(\\frac{2 c_{0}}{105} + \\frac{c_{1}}{84} + \\frac{c_{2}}{126}\\right)$"
      ],
      "text/plain": [
       "c0/5 + c1/5 + 6*c2/35 - lambda*(2*c0/105 + c1/84 + c2/126)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq2= diff(Phi,c2)\n",
    "eq2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "19071805-db55-4ac0-b6d1-99449c30a5e6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & 0 & 0\\\\0 & 0 & 0\\\\0 & 0 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[0, 0, 0],\n",
       "[0, 0, 0],\n",
       "[0, 0, 0]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix_c=zeros(3)\n",
    "matrix_c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "de5a1f7c-c568-49d8-9a61-42411ed5c9dd",
   "metadata": {},
   "outputs": [],
   "source": [
    "c = [c0,c1,c2]\n",
    "eqs = [eq0,eq1,eq2]\n",
    "for i in [0,1,2]:\n",
    "    for Phi in [0,1,2]:\n",
    "        matrix_c[i,Phi]= expand(eqs[i]).coeff(c[Phi])\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "26353137-749f-4f00-8fbc-7df8633c1c72",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{2}{3} - \\frac{\\lambda}{15} & \\frac{1}{3} - \\frac{\\lambda}{30} & \\frac{1}{5} - \\frac{2 \\lambda}{105}\\\\\\frac{1}{3} - \\frac{\\lambda}{30} & \\frac{4}{15} - \\frac{2 \\lambda}{105} & \\frac{1}{5} - \\frac{\\lambda}{84}\\\\\\frac{1}{5} - \\frac{2 \\lambda}{105} & \\frac{1}{5} - \\frac{\\lambda}{84} & \\frac{6}{35} - \\frac{\\lambda}{126}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[   2/3 - lambda/15,     1/3 - lambda/30, 1/5 - 2*lambda/105],\n",
       "[   1/3 - lambda/30, 4/15 - 2*lambda/105,    1/5 - lambda/84],\n",
       "[1/5 - 2*lambda/105,     1/5 - lambda/84,  6/35 - lambda/126]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix_c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "41ea76a9-df1f-4662-b538-903745ae24d0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - \\frac{\\lambda^{3}}{55566000} + \\frac{11 \\lambda^{2}}{3969000} - \\frac{17 \\lambda}{165375} + \\frac{2}{2625}$"
      ],
      "text/plain": [
       "-lambda**3/55566000 + 11*lambda**2/3969000 - 17*lambda/165375 + 2/2625"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix_c.det()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "4b7aea0c-06b2-4aec-a70b-83b5fa415006",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[56 - 4*sqrt(133), 42, 4*sqrt(133) + 56]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sol_lamd = solve(matrix_c.det(),lamd)\n",
    "sol_lamd.sort() # 排序\n",
    "sol_lamd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "1aed06f5-f346-4638-8e63-34717f301f01",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 4 \\sqrt{133} + 56$"
      ],
      "text/plain": [
       "4*sqrt(133) + 56"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sol_lamd[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "2805e586-4b89-4da4-8641-9284c575db05",
   "metadata": {},
   "outputs": [],
   "source": [
    "condition = integrate(y*y,(x, 0, 1)) -1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "f5f452d0-820a-46ce-927b-22cb3c1e44eb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(-sqrt(10)*sqrt(266 - 23*sqrt(133)) - sqrt(1330)*sqrt(266 - 23*sqrt(133))/19,\n",
       "  -3*sqrt(353780 - 30590*sqrt(133))/19,\n",
       "  sqrt(8820 - 14490*sqrt(133)/19)),\n",
       " (sqrt(1330)*sqrt(266 - 23*sqrt(133))/19 + sqrt(10)*sqrt(266 - 23*sqrt(133)),\n",
       "  3*sqrt(353780 - 30590*sqrt(133))/19,\n",
       "  -sqrt(8820 - 14490*sqrt(133)/19))]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 求 c0,c1 \n",
    "eqs_1=[eq0.subs(lamd,sol_lamd[0]), eq1.subs(lamd,sol_lamd[0]),\n",
    "       eq2.subs(lamd,sol_lamd[0]),condition]\n",
    "c_sols_1 = solve(eqs_1, c0,c1,c2)\n",
    "c_sols_1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "217615b0-b8c5-4d71-8649-cf10c54fa08a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(-sqrt(210), 2*sqrt(210), 0), (sqrt(210), -2*sqrt(210), 0)]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 求 c0,c1 \n",
    "eqs_2=[eq0.subs(lamd,sol_lamd[1]), eq1.subs(lamd,sol_lamd[1]),\n",
    "       eq2.subs(lamd,sol_lamd[1]),condition]\n",
    "c_sols_2 = solve(eqs_2, c0,c1,c2)\n",
    "c_sols_2 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "be5f236f-e65e-4833-ab5f-0b78eb28eb7b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(-sqrt(10)*sqrt(23*sqrt(133) + 266) + sqrt(1330)*sqrt(23*sqrt(133) + 266)/19,\n",
       "  3*sqrt(30590*sqrt(133) + 353780)/19,\n",
       "  -sqrt(14490*sqrt(133)/19 + 8820)),\n",
       " (-sqrt(1330)*sqrt(23*sqrt(133) + 266)/19 + sqrt(10)*sqrt(23*sqrt(133) + 266),\n",
       "  -3*sqrt(30590*sqrt(133) + 353780)/19,\n",
       "  sqrt(14490*sqrt(133)/19 + 8820))]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 求 c0,c1 \n",
    "eqs_3=[eq0.subs(lamd,sol_lamd[2]), eq1.subs(lamd,sol_lamd[2]),\n",
    "       eq2.subs(lamd,sol_lamd[2]),condition]\n",
    "c_sols_3 = solve(eqs_3, c0,c1,c2)\n",
    "c_sols_3 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "6ef2fbce-3548-4085-897c-716e5217dd7b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x22feb3c6650>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_1=y.subs([(c0,c_sols_1 [0][0]), (c1,c_sols_1 [0][1]),(c2,c_sols_1 [0][2])])# 基态试探解\n",
    "y_ex_1= sqrt(2) *sin(pi* x) # 基态精确解\n",
    "plot(y_1,y_ex_1,(x,0,1)) # ,legend=True\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "21b0d17d-aef0-4327-b326-c47f59d3bc22",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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DBvxyO2SU8z4iIlKhKZETp7341zrW7M4gqloQ467rTFhQgOs3yT0CP10P9gJocR70vNftcfozi8XCsxe2ZmTnejgMuO+7FUzfUM5FC0Negri25uKH8bfoeTkRkUpIiZw4ZfbG/Xy90Hxu690rO1KvZpjrNzEM+O1uOLwdatSHEWOr5OKG07FaLbxySTsuaB9PkcPgjq+Xs2jrQddvFBgCI7+AoOrmlmezXnF/sCIi4lNK5OS00nMLeXT8KgBu6NmQs5uW83m2he/Dhj/N7bdGfgGhNd0YZeVis1p487L2DG4VS0GRgzu+XsbOgzmu36hWE7ig+Hm52a9r5wcRkUpGiZyc1nN/rGNveh6Noqvx6NDE8t1k5yKY8rTZHvIS1O3kvgArqUCblXeu7Ei7epEczink5i+WkJlX6PqN2l4KnW/EfF7uNj0vJyJSiSiRk1OavDaV8ct3YbXA6yPbERpUjhIh2QfNmmaOIvMh/K63uD/QSiok0Ma467oQGxHMpn1Z3P99EnZHObbyGvoyxOp5ORGRykaJnJzUoewCHp9g1ou7rU8TOjeIcv0mDgf8citk7IZazcxpPj0X55LYiBA+urYLwQFWpm/Yx38nbXD9JoGhMPLzY56X+6/b4xQREe9TIidlMgyDJ39dzYGsAprHVufBQc3Kd6NFH8KWaRAQCpd9Ye4+IC5rn1CD10e2B8x9WX9amuL6TaKbHvO83GuwZbobIxQREV9QIidl+mPVXv5anUqA1cKbl3UgOKAcU6oHt8C058z20JcgtrV7g6xiLmgfX7r7w+MTVrN0+yHXb9L2Uuh8A2DAr3dBXrpbYxQREe9SIicn2JeRx1O/rgHgnv5NaVM30vWbOBzw+71QlAuN+hY/bC9n6oEBzRjWJo5Cu8HtXy0j5VA5VrIOfQWimkDmXpgyxv1BioiI1yiRk+MYhsFjv6wmPbeQNnUjuPuccm7BteRjc6/PwGpw4bt6Ls5NrFYLb1zWntbxERzMLuDWL5eSle/iwoXAULjwHbO97DPYNsf9gYqIiFcokZPj/Ja0h+kb9hFks/LmZR0ItJXjr8jh7TD1GbM96Fmo2cCdIVZ5YUEBfHx9F2LCg9mQmskD3yfhcHUla8NeR0dJ/7gPCnPdH6iIiHicEjkplZ1fxMt/rwfgvgFNaR5bjoUJhmFOqRZmQ4Nexft9irvViQzlo2s7ExRgZer6NF6bnOz6TQY9C+HxcGgrzHzZ/UGKiIjHKZGTUh/M3EJaRj4JUaHc0rtx+W6y7DPYNttcpXrhO2DVXzFP6Vi/Jq9d2g4wP7tflu9y7QYhkXD+m2Z7/ruwe7mbIxQREU/T/2UFgJRDOXw0ZysAT5zbipDAcqxSPbITJj9ltgc8bW4PJR41vENd7j7H/HN+7JfVrNuT4doNWgwzizQbxYtT7OXYOUJERHxGiZwA8OLE9RQUOTi7aS2GtI51/QaGAb/fBwVZkNAdut/u/iClTA8NasE5LWIoKHJw73fLySlwcfHD0P9CaBSkrYF5b3smSBER8QglcsL8zQeYtDYVqwWePr81lvKsMF3xFWydAQEhMHwsWMsxoiflYrVaeH1ke2IjgtmyP5tnfl/r2g2qx5glScDc8WH/RvcHKSIiHqFEroorsjt47s91AFxzVgNaxJVjgUP6bvjnCbN9zuMQXc5dIKTcalUP5q3LO2KxwI9Ld/Fb0m7XbtDuMmg6COwF5hSrw+GZQEVExK2UyFVx3y3eyYbUTGqEBTJqUPPy3WTiQ5CfAXU7Q4973BugOK1Hk1rcW1z374kJa9hxMNv5zhYLnP9/5l6sKQth6SceilJERNxJiVwVdiSngDemmNNoowY1p0ZYkOs3Sf4bNv4N1kBNqVYA9w1oRteGNcnKL+K+71ZQUOTCyFqNBBj4jNme+gwcKcd+riIi4lVK5Kqwt6Zu4khOIS1iw7mqW33Xb1CYB38/arZ73AW1W7o3QHFZgM3K21d0JDI0kJW70nnd1fpyXW6GhLPMRSt/PmguYhERkQpLiVwVlZyayVcLdwDw9AWtCCjPDg7z3oYjOyC8DvR5xM0RSnnF1wjl1eL6ch/N3srM5H3Od7ZazS3VbEGweQqs+tFDUYqIiDsokauCDMPguT/XYncYDGkdy9lNo12/yeEdMLe4mOzgFyC4unuDlDMypHUc1/cwt0Z76MeV7MvIc75zTHPoWzzSOvlJyM/0QIQiIuIOSuSqoKnr9zFv80GCAqw8cW6r8t3kn8ehKA8a9jYLykqFM/rclrSsE8HB7AIe/NHF/Vh73gdRjSF7H8x503NBiojIGVEiV8U4HAZvFD83ddPZjahfK8z1m2yaChv+BIsNhr1qrniUCick0Ma7V3YkNNDGvM0H+WDWFuc7BwTB4BfN9oKx5gisiIhUOErkqphJa1PZkJpJeHAAd/Qtx36qRfnwd/HzcN3vgNhyjuiJVzStXZ1nh7cG4M0pG1m245DznVsMg0Z9wJ4PU8d4KEIRETkTSuSqELvD4P+Ky43c1KtR+cqNLHgPDm2BarWh36NujlA8YWTnegzvEI/dYXDfd0mk5zi5n6rFAkNeBosV1k6AHQs8G6iIiLjMLxO52bNnc8EFFxAfH4/FYuHXX389bZ+ZM2fSqVMngoODadq0KZ9//rnH46xoJq7ey6Z9WUSEBHBTr0au3yB9F8x+3WwPfh5CIt0boHiExWLhhRFtaFArjN1Hcnnsl1UYzpYViWsDna4z25Me044PIiIVjF8mctnZ2bRv356xY8c6df22bds477zzOOecc0hKSuKBBx7glltu4Z9//vFwpBWH3WHw1lRzNO7W3o2JDA10/Sb/PAGFOWadsXaXuzlC8aTwkEDevbIjgTYLf69J5VdXtvA65wkICoe9SbDqB4/FKCIirrMYTv/TvGKyWCxMmDCBESNGnPSaRx99lIkTJ7JmzZrSY1dccQVHjhxh0qRJZfbJz88nPz+/9H1GRgYJCQmkp6cTERHhtvi9ZcKKXTz4w0pqhAUy55FzCA9xMZHbOhO+HG5Os902C+q080ic4lnvTd/E65M3EhkayJQH+1A7IsS5jnPfMp+TC68D9y6DoGoejVNERJzjlyNyrlqwYAEDBw487tiQIUNYsODkz/y8/PLLREZGlr4SEhI8HabHFNkdvD11EwC39WnsehLnsMM/T5rtLjcrifNjd/RtQtu6kaTnFvL4hDXOT7GedSfUbAiZe81C0CIiUiFUiUQuNTWV2NjY447FxsaSkZFBbm5umX1Gjx5Nenp66SslxX/3nZywYjfbD+YQVS2I63s0dP0Gq36EtNUQHAnnPO72+MR7AmxWXhvZjkCbhanr0/gtaY+THYNh0HNme97b2odVRKSCqBKJXHkEBwcTERFx3MsfFdodvDPdHI27vU9jqgUHuHiDXJj+gtnu/SCERbk5QvG2xLgI7h/QDIAxv69lX6aTuz60vBAanG0Wgp72rAcjFBERZ1WJRC4uLo60tLTjjqWlpREREUFoaKiPovKO8ct2kXIol+jqQVxbvGWTSxZ9CBm7IKKeWTdOKoXb+zahTd0I0nMLecLZKVaLBYa8BFhg9U+QssTjcYqIyKlViUSuR48eTJs27bhjU6ZMoUePHj6KyDsKihy8O30zYD4bFRbk4mhc9sGj2zP1fxICK3fSW5UE2qy8PrI9gTYLU9al8ftKJ6dY4ztAh6vN9qTHwL/XSomI+D2/TOSysrJISkoiKSkJMMuLJCUlsXPnTsB8vu26664rvf6OO+5g69atPPLII2zYsIH333+fH3/8kQcffNAX4XvNhBW72H0kl5jwYK45qxyjcXNeh/wMiG0L7S5zf4DiU4lxEdzXvxxTrAOegsBqsHsprP7ZgxGKiMjp+GUit3TpUjp27EjHjh0BGDVqFB07duTpp58GYO/evaVJHUCjRo2YOHEiU6ZMoX379rzxxht8/PHHDBkyxCfxe4NhGHw8ZxsAt/ZuREigzbUbHNoGi8eZ7cHPgdXF/uIX7uhnTrEeyXFhijU8znxeEmDqM1CQ49EYRUTk5Py+jpy3ZGRkEBkZ6Td15GYm7+OGz5ZQPTiA+aP7E+FqyZGfb4I146FJf7h2gmeClAph/d4MLnxvLoV2g7ev6MDwDnVP36kwF97rCukpZsHgvo94PlARETmBX47IyemVjMZd3jXB9SRu9zIzicNytOSEVFot60Rwr6tTrIGhMKh45erc/4MMJ5+xExERt1IiVwmt35vB3M0HsFrghp4NXetsGDDZnKKm/ZUQ19bt8UnFc2e/JrSON6dYn3R2irX1xZDQ3dy2bfqLng9SREROoESuEvpkrjkaN6xtHRKiwlzrvPEf2DEXbMHQ/wkPRCcVUckq1gCrhcnOrmItLUcCrPwWDmzybJAiInICJXKVzL6MPH4r3hD9ll6NXOtsLzL30wRzS6bIem6OTiqyY6dYn/1jHYezC07fqV4XaHEuGA6Y+bKHIxQRkX9TIlfJfLlgB4V2gy4NatKxfk3XOid9A/s3QGgU9B7lmQClQrvrnCa0iA3nUHYB/520wblOJdu2rRkPqWs8F5yIiJxAiVwlklNQxNeLdgBwS28XR+OK8mHWq2a7z38gJNLN0Yk/CLRZeeGiNgB8vySFpdsPnb5TXFtofZHZ1qiciIhXKZGrRMYv382RnELqR4UxqFWca52Xf2luxRVeB7rc7JkAxS90bRjF5V0SAHhiwhoK7Y7Td+o3GixW2PAn7F7u4QhFRKSEErlKwuEw+LR4kcNNZzfEZrU437kwF+a8YbZ7PwSBIR6IUPzJY8MSiaoWRHJaZunimVOKaQHtLjfbM7SCVUTEW5TIVRLTNuxj24FsIkICGFk8muK0ZZ9D5l6ITIBO1532cqn8alYL4vFzWwLw1tSNpBxyYveGvo+CNQA2T4UdCzwcoYiIgBK5SuPjOVsBuKp7A6oFBzjfsSAH5rxptvv8BwKCPRCd+KNLOtWle6Mo8godPPP72tPXlotqBB2vNdvTnzdrEoqIiEcpkasEVu9KZ9G2QwRYLa4XAF7yMWTvgxoNoMPVHolP/JPFYuHFi9oQaLMwbcM+/lmbdvpOfR42axDumAdbZ3o8RhGRqk6JXCXw8VxzNO6C9vHERbrwfFt+Jsx7y2z3fRRsLm7lJZVe09rh3NanMQDP/rGWrPyiU3eIrAtdbjLb01/QqJyIiIcpkfNze47kMnHVXgBudrUA8OKPIOcgRDU5+qC6yL/c278Z9aPC2Juex1tTNp6+Q68HITAMdi81dwoRERGPUSLn576Yv50ih0GPxrVoU9eF2m956TDvHbPd7zGwufBcnVQpIYE2nhveGoDP5m9n7Z70U3cIj4Vut5ntGS+Aw4nyJSIiUi5K5PxYVn4R3y7eCcCtfVwcjVv4IeQdgegW0OYS9wcnlUq/FrU5r20d7A6DJyaswe44zZTp2fdDcASkrob1v3snSBGRKkiJnB/7LWk3mXlFNI6pRr/mtZ3vmHsYFow12/0eA6vNMwFKpfLU+a2oHhxAUsoRviv+B8RJhUVBj7vN9oyXwGH3fIAiIlWQEjk/9v3iFACu6lYfqysFgBeMhfx0qN0aWo3wTHBS6cRFhvDQ4OYA/HfSBvZn5p+6w1l3QmhNOJAMq3/2QoQiIlWPEjk/tWZ3Oqt3pxNks3Jxp3rOd8w+CAs/MNvnjAar/gqI867r0ZC2dSPJzCvihYnrTn1xSCT0vNdsz3ldo3IiIh6g/4v7qe+XmFNbQ9rEEVUtyPmO89+BgiyIaweJ53soOqmsbFaztpzFAr8l7WHxtkOn7tD1VjOhO7BRz8qJiHiAEjk/lFNQxG8r9gBwZVcXtuPKOWQWAAY453GwuDAdK1KsXb0aXNG1PmDWljvlwoeQCOh+p9me/brqyomIuJkSOT80cdVeMvOLqB8VxlmNaznfcfFH5mhcbBtoPtRzAUql95/BzQkPCWDtngx+XJpy6ou73w5B1SFtDWyc5J0ARUSqCCVyfuj7Jeb/OC/vmuD8Iof8zKPPxvUepdE4OSO1qgfzwEBz4cNr/ySTnlt48ovDoqDbrWZ79msalRMRcSMlcn5mY1omy3Ycxma1MLKzC4scln5m1o2r1VQrVcUtruvRgCYx1TiUXcA70zad+uKz7oaAUNi9DLbO8E6AIiJVgBI5P1NScmRAYm1qRzi5r2phHix4z2z3elB148QtAm1Wnr7A3PHhi/nb2bwv8+QXV4+BLjea7dmveyE6EZGqQYmcH8krtPPLil0AXNmtvvMdk76GrDSIqAdtL/NQdFIV9W0ew8CWtSlyGDz353qMU02b9rwXbEGwYx5sn+e9IEVEKjElcn7kn7WpHMkpJD4yhD7NY5zrZC+EuW+b7bPvhwAXSpWIOOHJ81oRaLMwe+N+pm/Yd/ILI+Kh4zVme/Zr3glORKSSUyLnR0qmVUd2ScDm7CKH1T9D+k6oFgOdrvVgdFJVNYyuxk29zL1+n/9zHflFpyj8e/YDYLGZz8ntWuqdAEVEKjElcn5i+4FsFmw9iMUClzlbO87hgLlvmu0ed0NgqOcClCrt3v7NiAkPZvvBHD6ft/3kF9ZsAO2vMNt6Vk5E5IwpkfMTJSVH+jaPoW4NJxOyDX+YFfVDIqHLzR6MTqq66sEBPDKkBQDvTt/Mvsy8k1/caxRggY1/w95V3glQRKSSUiLnBwrtDn5eZi5yKKmof1qGcXTEo9vtZoV9EQ+6pFM92ifUICu/iNcmJZ/8wuim0OZisz1Ho3IiImdCiZwfmLY+jQNZ+URXD2ZAy9rOddo8DVJXQWA1OOtOzwYoAlitFsZc0AqAn5btYmXKkZNf3Ps/5td1v8PBLZ4PTkSkklIi5we+K13kUI9Am5MfWclIR5cbzcr6Il7QqX5NLu5YF4Bn/liL42T7sMa2Kt4mzoD573ovQBGRSkaJXAW3+0guszftB+AKZxc57JgPOxeYNbt63OPB6ERO9OiwRMKCbKzYeYTfVu4++YU97zO/Jn0LWacoWyIiIielRK6C+y1pN4YBZzWOokGtas51Knk2ruM1EFHHc8GJlCE2IoS7z2kKwCt/byA7v6jsCxv0hLpdwJ4Piz/yYoQiIpWHErkK7vekPQCM6FDXuQ57V8KWaWatrpIRDxEvu7lXI+pHhZGWkc+Hs07yDJzFYhapBlg8DvKzvBegiEgloUSuAtuQmsGG1EyCbFaGtXFyZG1+8Z6qrS+CqEaeC07kFEICbTx+bksAxs3ZSmr6ScqRJJ4HUU0g7wis+Mp7AYqIVBJK5Cqw34pH4/q1iCEyLPD0HdJ3wZrxZrvnvR6MTOT0hrSOpUuDmuQVOnhj8knKkVhtR/+uLhhrbiknIiJOUyJXQTkcRum06nBnp1UXfgCGHRr1gfgOngtOxAkWi4UnzjNH5X5evot1ezLKvrD9leYWcukpsHaCFyMUEfF/SuQqqOU7D7P7SC7VgmzO1Y7LS4dlX5htPRsnFUTH+jU5v10dDANe/nt92RcFhkD3O8z2vLfNYtYiIuIUJXIVVMm06pA2cYQE2k7fYdnnUJAJMYnQdKBngxNxwSNDEgm0WZiz6QCzNu4v+6KuN5vFq9PWmIt1RETEKUrkKqBCu4OJq/cCTk6rFhXAwg/Nds97zdWAIhVE/VphXN+jIQAvTVyPvawiwaE1ofP1ZnveO94LTkTEzymRq4DmbjrAoewCoqsHcXaTWqfvsGY8ZO6B6nHQdqTnAxRx0T39mxIZGkhyWiY/L0sp+6Kz7jLL5mybBXtWeDdAERE/pUSuAvotyayGf367eAJOtyWXccwWR91vh4BgD0cn4roaYUHc298sEvzG5I3kFJRRJLhGArS91GxrVE5ExClK5CqYnIIiJq9LA+DCDvGn77BlOuxbaz5f1OVGD0cnUn7X9mhAQlQo+zLzGTd7W9kXlSzUWfcrHDrJNSIiUkqJXAUzdf0+cgrsJESF0jGhxuk7lIzGdbrOfM5IpIIKDrDx6NBEAP43ewv7MssoEhzXxlysYzjMunIiInJKSuQqmN9WmNOqw9vXxXK6RQt7V8HWGeZzRWfd6YXoRM7MeW3r0CGhBjkFdv5vyqayLyrZtmvF15B9wHvBiYj4ISVyFcjh7ILS8gwjOjoxrbqgZDuuEVCzgecCE3ETi8XCk8VFgn9YspONaZknXtSwN8R3hKJcWPKJlyMUEfEvSuQqkL/W7KXIYdCqTgRNa4ef+uJjt+PqcY/ngxNxky4NoxjaOg6HAS//VUaRYIvl6N/pJR9DUb53AxQR8SNK5CqQ30q35HJiNG7hB+AoMkcv6nbycGQi7vXosEQCrBZmJO9n/pYypk9bDYfweMjeB2t+8X6AIiJ+QolcBbHnSC6Ltx0C4IL2p0nkjtuO614PRybifo2iq3F19/oA/PfvDRj/3pbLFgjdbjXbC8dq2y4RkZNQIldB/L7SHI3r1iiK+Bqhp7542RfmdlzRLaDpIC9EJ+J+9/RvRliQjZW70vl7TeqJF3S+AQJCIXU1bJ/r9fhERPyBErkKomRadcTptuSyF8Kiku247gGrPkLxTzHhwdzSuzEAr/+TTJHdcfwFYVHQ4UqzvfADL0cnIuIflAVUABvTMlm/N4NAm4VhbeJOffH6PyBjN4RFQ9vLvBOgiIfc2rsRUdWC2Hogmx+X7jrxgu7FZXWS/4KDW7wbnIiIH1AiVwH8Xjwa17d5DDWrBZ364kX/M792uQkCQzwcmYhnhYcElm7d9dbUjeQW2I+/IKZ58eMDBiz+yPsBiohUcErkfMwwDP5YZSZyp13ksGcFpCwEawB0vdkL0Yl43lXd61Ovprl116fzytiWq8dd5tcVX5sLfUREpJQSOR9LTstkx8EcggKsDGwZe+qLFxY/G9f6Igg/zRSsiJ8IDrDx0ODmAHw4awtHcgqOv6DxORDTEgqyYPlXPohQRKTiUiLnY5PXpgHQu2k01YIDTn5hZtrRAsDdtR2XVC7D29clMS6czLwi3p/5r2fhLJajW9At+h/Yi7wfoIhIBaVEzscmrzPLLgxufZrRuKWfgqMQ6nWFep29EJmI91itFh4dmgjA5/O3s+dI7vEXtLsMwmpB+k5InuiDCEVEKiYlcj60+0gua3ZnYLXAgFNNqxblw9LiPSe73+Gd4ES8rF+LGLo3iqKgyMH/Tdl4/MnAUHOBD8CC970fnIhIBaVEzoemrDVH47o0iCK6evDJL1zzC2TvN7csajXcS9GJeJfFYuHRYeao3Pjlu9iUlnn8BV1vAWugueBn9zIfRCgiUvEokfOhyevM5+NOOa1qGEcLAHe92dy6SKSS6lS/JkNax+Iw4NV/ko8/GR4HbS4x2yoQLCIC+HEiN3bsWBo2bEhISAjdu3dn8eLFJ732888/x2KxHPcKCfFtDbbD2QUsKt5bdVCrUyRyKYtgbxIEhEDnG70TnIgPPTwkEasFpqxLY/nOw8efLFn0sHYCZOzxfnAiIhWMXyZyP/zwA6NGjWLMmDEsX76c9u3bM2TIEPbt23fSPhEREezdu7f0tWPHDi9GfKLpG/ZhdxgkxoXToFa1k19YMvLQdiRUq+Wd4ER8qGnt6lzSqR4Ab0z+16hcfAdocDY4imDxOO8HJyJSwfhlIvfmm29y6623cuONN9KqVSs+/PBDwsLC+PTTT0/ax2KxEBcXV/qKjT31KtH8/HwyMjKOe7lT6WrVU43Gpe8yt+QCLXKQKuW+Ac0ItFmYt/kg8zcfOP5kyajcss+gIMf7wYmIVCB+l8gVFBSwbNkyBg4cWHrMarUycOBAFixYcNJ+WVlZNGjQgISEBIYPH87atWtP+X1efvllIiMjS18JCQlu+xlyC+zM2rgfgMGtT1HYd/E4MOzQsDfEtXHb9xep6BKiwriqW30AXpucjGEYR0+2OBdqNoTcw7DqB98EKCJSQfhdInfgwAHsdvsJI2qxsbGkpqaW2adFixZ8+umn/Pbbb3z99dc4HA569uzJrl1lbNJdbPTo0aSnp5e+UlJS3PYzzN18gLxCB/GRIbSOjyj7ooIcWPa52dZonFRBd/dvSkiglRU7jzBt/TGPTVht0PVWs734I3NBkIhIFeV3iVx59OjRg+uuu44OHTrQt29ffvnlF2JiYvjf//530j7BwcFEREQc93KXyWtLigDHYbFYyr5o9Y+QdwRqNIAWw9z2vUX8Re3wEG7o2QiA1ycn43Ack7B1vAYCw2DfOtg+10cRioj4nt8lctHR0dhsNtLS0o47npaWRlycc/uPBgYG0rFjRzZv3uyJEE+pyO5g6vrTlB0xjKP7qna7zRyBEKmC7ujbmPDgADakZvLn6r1HT4TWgHaXm+3FH/kkNhGRisDvErmgoCA6d+7MtGnTSo85HA6mTZtGjx49nLqH3W5n9erV1KlTx1NhntSyHYc5nFNIZGgg3RpGlX3Rtlmwfz0EVjNHHkSqqBphQdzapzEA/zdlI0V2x9GT3W4zv26YaC4MEhGpgvwukQMYNWoU48aN44svvmD9+vXceeedZGdnc+ONZp216667jtGjR5de/9xzzzF58mS2bt3K8uXLueaaa9ixYwe33HKL12P/Z605GjegZW0CbCf54y8ZjetwlTnyIFKF3dSrEVHVgth2IJvxy49J2GJbmQuBDDss+cR3AYqI+JBfJnKXX345r7/+Ok8//TQdOnQgKSmJSZMmlS6A2LlzJ3v3Hp2GOXz4MLfeeistW7bk3HPPJSMjg/nz59OqVSuvxm0YxjFlR04yDXxoK2ycZLa73+6lyEQqrurBAdzVrwkAb0/dRH6R/ejJklG55V9AYZ4PohMR8S2LYWjJlzMyMjKIjIwkPT293Asf1u3J4Nx35hAcYGXF04MICwo48aK/H4NFH0DTQXDNz2cYtUjlkFdop99rM0nNyGPMBa248WxzEQT2Ini7PWTsguHvQ8erfRuoiIiX+eWInL8qGY3r3Sym7CQuLwNWfG22z1LJEZESIYE27hvQDICxMzaTU1BknrAFmHsQAyz+n0qRiEiVo0TOiyavPc1q1ZXfQ0Em1GoGjft7MTKRim9kl3o0qBXGgawCPpu3/eiJTteDLRj2roRdS3wWn4iILyiR85KUQzms25uB1QIDEmufeIFhwJKPzXa328Cqj0bkWIE2Kw8ObA7A/2ZtIT230DxRrZa5FzHAopPXhhQRqYyULXjJlHXmaFzXhlHUqh584gXbZsOBZAiqDu2v8HJ0Iv7hgvbxNI+tTkZeEeNmbz16olvxTg/rfoXMsnd4ERGpjJTIeUnpatWT7a26ZJz5td3lEOK+XSREKhOb1cJDg1sA8Om8bRzIyjdPxHeAhO7gKIKln/kuQBERL1Mi5wWHsgtYvO0QAINblfF8XPpu2PCX2S4ZWRCRMg1uFUu7epHkFNj56LhRueJSJMs+g6IC3wQnIuJlSuS8YNr6NBwGtKwTQUJU2IkXLPvMLGraoBfUbun9AEX8iMVi4cFB5rNyXy7Yzv7M4lG5VsOhehxkpcH6330YoYiI9yiR84LJxc/HlTkaV1QAy74w2yVlFETklPo1j6FDQg3yCh18OGuLedAWCF1uMtta9CAiVYQSOQ/LLbAzZ9N+4CRlR9b/Dtn7zJGElhd4OToR/2SxWBhVPCr39cIdpGUU7+rQ+QawBsKuxWY5EhGRSk6JnIfN3rSfvEIHdWuE0qpOGYsYSkqOdL7BHFEQEaf0bhZNlwY1yS9y8MHM4lG58Nij/yDS/qsiUgUokfOwkiLAQ1rHYbFYjj+ZugZ2LgBrgJnIiYjTjh2V+3bRTvam55onut5ifl39E+Sl+yg6ERHvUCLnQXaHwfQNZiI3qKzn40pKjiSeDxF1vBiZSOXQo0ktujWKosDu4P0ZxaNyDXpCTEsozDF3SxERqcSUyHnQql1HOJxTSHhwAF0a1jz+ZO4RWPWj2VbJEZFyOXZU7vslO9l9JBcslqMLh5Z8ov1XRaRSUyLnQbM2moscejWLJtD2rz/qld+ZIwYxLaHB2T6ITqRyOKtxLXo2qUWh3eC96ZvNg+0uh8Bq5m4p2+f6NkAREQ9SIudBJYlc3+Yxx59wOI7ZV/UWcwRBRMqtpK7cT0tTSDmUY+6O0u4y8+RSLXoQkcpLiZyHHM4uICnlCAB9W/wrkds2Ew5uhqBwc+RARM5I14ZR9G4WTZHjmFG5kunV9X9o/1URqbSUyHnInM0HMAxoERtOncjQ408uLh6N63AlBId7PziRSqhkVO7n5bvYcTAb4toe3X91+Vc+jk5ExDOUyHnIrOTiadV/j8YdSYGNf5vtkjIJInLGOtWvSb8WMdgdBu9MKx6V61I8KrfsM7AX+S44EREPUSLnAQ6HUfp8XL9/Px+39FMwHNCwN8S08EF0IpXXgwPNUbkJK3axdX+Wuf9qWC3I2A2b/vFxdCIi7qdEzgPW7c3gQFY+YUE2Oh9bdqQoH5Z/abZVckTE7don1GBgy9o4DHhn2iYIDIGO15gnSxYYiYhUIkrkPKBkNK5nk1oEB9iOnlj7K+QcgPB4aHGeb4ITqeQeKB6V+33lHjbvy4TONwIW2DIdDm7xbXAiIm6mRM4Djj4fV/v4EyUjAl1uBFuAl6MSqRra1I1kcKtYHAa8PW0zRDWCpgPNk0s/9W1wIiJupkTOzTLyClm28zDwr+fjUlfDrsXmvqqdrvNRdCJVQ8mo3J+r9pCcmnm0FEnSN1CY68PIRETcS4mcm83bdAC7w6BxTDUSosKOnlj6mfk18XwIj/NNcCJVRKv4CM5tG4dhwNvTNkKzwRCZALmHYe0EX4cnIuI2SuTcrMzdHPIzYdUPZrvLTT6ISqTquX9AcywW+Gt1KutSs6HzDeaJJdrpQUQqDyVybmQYRtmJ3OqfoSALajWFRn18FJ1I1dIiLpzz2tYBikflOl0H1kDYvRT2JPk2OBERN1Ei50Yb07LYm55HcICVsxrXMg8axtEHrDvfqH1VRbzogYHNsFjgn7VprEkPhlYXmie0/6qIVBJK5Nxo1sZ9AJzVuBYhgcVlR3Yvh9RVYAuGDlf5MDqRqqdp7XCGt48H4K2pG4/uprLqJ8g94rvARETcRImcG5Xu5nDstlwlo3GtL4KwKB9EJVK13TegGVYLTF2/j5WWlhDTEopyYeX3vg5NROSMKZFzk+z8IpZsM8uOlD4fl3sY1ow321rkIOITjWOqc1HHegC8NW3T0VIkSz8xH30QEfFjSuTcZMGWgxTYHSREhdIoupp5cOUP5r/8a7eGhG6+DVCkCrtvQFNsVgszkveTFDUEAqvBgY2wfY6vQxMROSNK5NykdFq1eW0sFsvxixy6aJGDiC81qFWNSzrVBeCNWXuh/eXmCe2/KiJ+TomcGxiGwczihQ6l06o75sOBZPNf/u0u92F0IgJwb/9mBFgtzNl0gHV1R5oHN0yEjL2+DUxE5AwokXODbQeySTmUS5DNSo8mxWVHSkbj2l4KIRG+C05EAEiICuOSTuazcq+sCICEs8BRBMu/9HFkIiLlp0TODeZuPgBAl4Y1qRYcAFn7Yd1v5skuN/owMhE51t3nmM/Kzd64n22NrzAPLvsc7EU+jUtEpLyUyLnB/M0HATi7abR5IOkbcBRCfCeI7+jDyETkWPVrhZU+K/fC1mYQVgsy98DGST6OTESkfJTInSG7w2DBVjOR69GkFjgcsOwz86RKjohUOPec0wyb1cK0TemkNSl+Vk6LHkTETymRO0Pr92aQnltI9eAA2tWNhK0z4PB2CI6ENhf7OjwR+Zf6tcK4uKM5KvfawZ6Axfy9PbjFt4GJiJSDErkzNH+L+Xxc90ZRBNisRxc5tL8Cgqr5MDIROZl7+pvPyv28NYD0ev3MgyW/uyIifkSJ3Bmat/mYadWMPZD8t3lCixxEKqwGtapxUfGo3Kf5/c2DSd9AYa4PoxIRcZ0SuTNQUORgyfZDQPFCh+VfgWGH+j2hdksfRycip3JP8QrWd1MaUVCtrrmlXslqcxERP6FE7gys2nWEnAI7UdWCaBETCsu/ME9okYNIhdcw2hyVc2Dlj8BB5kFNr4qIn1EidwbmbymeVm1cC+vmKZCx2yxn0OpCH0cmIs4oGZV7JbUrhiUAUhZB6hpfhyUi4jQlcmdgXnEh4J5Nax39l3yHqyEg2IdRiYizGkZXY0SHuuynJktDe5oHS8oHiYj4ASVy5ZRbYGfFziMA9InJgc1TzROdb/BZTCLiunv6N8Vqgf870ss8sPIHyM/ybVAiIk5SIldOy3YcpsDuoE5kCPW2/ggY0PgcqNXE16GJiAsaRVdjRMe6LHC0IjWgLhRkwpqffR2WiIhTlMiV07zi+nG9G0diWfGVeVCLHET80r39m2GxWPkkt695QIseRMRPKJErp5KFDheHJUH2fqgeBy2G+TYoESmXRsXPyv1s70MhgbB3Jexe7uuwREROS4lcOWTkFbJ61xEAOqb9Yh7sdB3YAn0XlIickXv6NyXdEsGf9m7mAY3KiYgfUCJXDou3HsJhQJ+owwTvmgcWq5nIiYjfahxTneEd6vJN0QDzwJrxkHvEpzGJiJyOErlyKHk+7raw2eaBZkOgRoIPIxIRd7inf1OW04JkRz0ozIFVP/o6JBGRU1IiVw4LthwkmAK6pU8yD2iRg0il0CSmOsM71OMbe/Go3NJPwTB8G5SIyCkokXPRwax8NqRmcp51IUGF6RBZH5oO8HVYIuIm9/Rvym+O3uQYwbB/Pexc6OuQREROSomcixZvOwTAzaGzzAOdrwerzYcRiYg7NYmpzjntm/K7vYd5QIseRKQCO6NErrCwkJSUFJKTkzl06JC7YqrQFm07RKJlJ63t68EaAB2v9XVIIuJm9/RvxreOgQA41v4K2Qd9G5CIyEm4nMhlZmbywQcf0LdvXyIiImjYsCEtW7YkJiaGBg0acOutt7JkyRJPxFohLN52kKts08w3iedDeKxvAxIRt2tauzqN2vVilaMRVkcBJH3j65BERMrkUiL35ptv0rBhQz777DMGDhzIr7/+SlJSEhs3bmTBggWMGTOGoqIiBg8ezNChQ9m0aZOn4vaZ/YcOc5FtrvlGixxEKq17+zfjW7s5Kpe/6BNwOHwckYjIiQJcuXjJkiXMnj2b1q1bl3m+W7du3HTTTXz44Yd89tlnzJkzh2bNmrkl0IriXNsiwi25UKspNOrj63BExEOa1q5OUauLyNj4NREZ22HbLGhyjq/DEhE5jsUwyre2PjMzk/DwcHfHU2FlZGQQGRnJgkdac1ZoCgx+EXre4+uwRMSDNu/LZP67N3KdbQrpjYYRef33vg5JROQ45V7s0Lt3b1JTU90ZS4VWku+2su7EYQ2CDlf5OCIR8bSmtcPZ1eRKAKpv+wcy9vo4IhGR45U7kevYsSPdu3dnw4YNxx1PSkri3HPPPePAKpptB7NL20briyAsyofRiIi3jBw2mCWO5thwsG/2x74OR0TkOOVO5D777DNuuOEGevXqxdy5c9m4cSOXXXYZnTt3xmbzfF21sWPH0rBhQ0JCQujevTuLFy8+5fU//fQTiYmJhISE0LZtW/766y+Xvt/yjTtK27auN5crZhHxP81iw1kXfykAAUlfgsPu44hERI46ozpyzz77LKNGjWLQoEG0adOGzMxMFixYwB9//OGu+Mr0ww8/MGrUKMaMGcPy5ctp3749Q4YMYd++fWVeP3/+fK688kpuvvlmVqxYwYgRIxgxYgRr1qxx+nta14wH4GBoY0jo5pafQ0T8w9kX3MRhozpRRftIWfybr8MRESlV7sUOaWlpvPTSS4wbN46WLVuyYcMGPv30Uy6//HJ3x3iC7t2707VrV9577z0MwyA9PZ2WLVty++23M2rUqBOuv+GGG8jOzuann34qPda/f3/atWvHW2+9Veb3yM/PJz8/HwCHw8HOtwbQ+/82s/DLZ2k5/AFP/FgiUoHN/OBe+h2ZwNrQrrR+YIKvwxERHzAMgxXvXU1+TFtaD7udiEjPP2YVHh6OxWI5ZVDlEhoaanTo0MH4888/DcMwjL///tuIiIgwXn311fLe0in5+fmGzWYzJkyYYBiGYaSnpxuAXnrppZdeeumlV6V7paennzIvcqmO3LE+/fRTrrjiitL3Q4cOZcaMGZx//vls376dsWPHlvfWp3TgwAHsdjuxseaOCuHh4aSnp/PUU08xb948pk+ffkKfWrVq8eGHHzJy5MjSY+PGjeOVV15hy5YtZX6fY0fkDh8+xLp/PuWKh99m3bp11K1b1wM/mZRXRkYGCQkJpKSkEBER4etw5BiV7bPZ+NZ5NM9dyZQalzHozjd9Hc4Zq2yfT2Wiz6Zi2vLFnTTZ8we/ZbTgnNETvPLZnK7UW7kTuWOTuBKdOnVi/vz5DBs2rLy3dZnFYiEiIoLg4GBsNluZf6gWi4WwsLDjzoWGhmK1Wp36EOrVq0fNmv+Bh98mPDxcv1QVVEREhD6bCqqyfDZ1BtxFxJQ76JMzmT2ZhSTWreXrkNyisnw+lZE+mwokL51Wh6YSHGzh2+1RDK8gn80ZLXYoS8OGDZk/f767b1sqOjoam81GWlraccfT0tKIi4srs09cXJxL14uIlKXuWZeSbosixpLOnD++8HU4IuJFjpU/EmzksclRlxkrd/o6nFIuJXI7dzoXeM2aNQHYvXu36xGdRlBQEJ07d2batGmlxxwOB9OmTaNHjx5l9unRo8dx1wNMmTLlpNeLiJTJFkhR+2sAaLn7Z5JTM30ckIh4hWFQsOgTAH5kIPl7N/s4oKNcSuS6du3K7bffzpIlS056TXp6OuPGjaNNmzaMHz/+jAMsy6hRoxg3bhxffPEF69ev58477yQ7O5sbb7wRgOuuu47Ro0eXXn///fczadIk3njjDTZs2MAzzzzD0qVLuece57fYCg4OPu6rVBzBwcGMGTNGn00FVBk/m1p9bsWBhV62tXz/94nP5PqTyvj5VBb6bCqYXUsJObSePCOQnfUuYMxTT1SYz8al8iM33XQTNWvW5JNPPiEkJITOnTsTHx9PSEgIhw8fZt26daxdu5ZOnTrx1FNPeXSHh/fee4/XXnuN1NRUOnTowDvvvEP37t0B6NevHw0bNuTzzz8vvf6nn37iySefZPv27TRr1oxXX33VpfhK9lpNT0+vEHPiIuI7WZ9eTPWd0/io6Dz63vM/WsRVnX2nRaqkCXfCym/52d6HgwPf4va+TXwdUSmXErmgoCBSUlIIDw8nJiaGK6+8koMHD5Kbm0t0dDQdO3ZkyJAhtGnTxpMx+4QSOREplTwJvrucw0Z1nmk2nrevOcvXEYmIp+QexngjEUtRHhflP8tzd99I23qRvo6qlEurVuPj40lKSmLIkCHk5uby0ksvUbt2bU/FJiJSMTUbRGH1eGpm7cG6/jc2prWmeaxG5UQqpZXfYynKY72jPluCE2kVX7EGc1x6Ru6hhx7iggsuoHfv3lgsFr755huWLFlCbm6up+ITEal4rDYCu5rP5F5pm8Y70zb5OCAR8QjDgKWfAfCNfQBnNY7GZj3FLgs+4FIid++997J06VKGDh2KYRiMHTuWHj16EBERQcuWLbniiit45ZVX+Pvvvz0Vr4hIxdDxWgyLjW7WZDatWczGNK1gFal0di6AA8nkWUL41X42PZtUvNqRLteRa9euHU888QRNmjRh4cKFZGZmMnfuXB544AFq1qzJb7/9xmWXXeaJWEVEKo6IOlgSzQVTV1o1KidSKS39FIDf7T3JIoyeTaN9HNCJyl0QeNOmTURHRxMaGkr37t25/fbb+eCDD1iwYAEZGRnujNFrxo4dS8OGDQkJCaF79+4sXrz4lNf/9NNPJCYmEhISQtu2bfnrr7+8FGnV48pnM27cOHr37k3NmjWpWbMmAwcOPO1nKeXn6u9Nie+//x6LxcKIESM8G6AndbkJgIttc5i+ehubKtionKufzZEjR7j77rupU6cOwcHBNG/eXP9d8yBXP5+33nqLFi1aEBoaSkJCAg8++CB5eXleirbqmD17NhdccAFtGtUhf8WPAHxZ2J/o6kE0q129zD4zZ86kU6dOBAcH07Rp0+OqZnia23d2AHNLLH/zww8/MGrUKMaMGcPy5ctp3749Q4YMYd++fWVeP3/+fK688kpuvvlmVqxYwYgRIxgxYgRr1qzxcuSVn6ufzcyZM7nyyiuZMWMGCxYsICEhgcGDB3ukQHVV5+pnU2L79u385z//oXfv3l6K1EMa9YOajYiw5HK+dQHvTK84RUJd/WwKCgoYNGgQ27dv5+effyY5OZlx48Zpb2kPcfXz+fbbb3nssccYM2YM69ev55NPPuGHH37g8ccf93LklV92djbt27fnu8cuIDjAwg5bI9YYjenRJLrM/Gbbtm2cd955nHPOOSQlJfHAAw9wyy238M8//3gnYEMMwzCMbt26GXfffXfpe7vdbsTHxxsvv/yyYRiGkZ6ebgBGenq6YRiGcdlllxnnnXfecffo3r27cfvtt3sv6CridJ/N6RQVFRnh4eHGF1984akQq6zyfDZFRUVGz549jY8//ti4/vrrjeHDh3shUg+a+5ZhjIkwkp7qYDR87E9jU1qGryMyDMP1z+aDDz4wGjdubBQUFHgrxCrN1c/n7rvvNvr373/csVGjRhlnn322R+OsshwOw3i7o2GMiTBef+5Bo8GjfxrfLtpR5qWPPPKI0bp16+OOXX755caQIUO8EanhkRE5f1NQUMCyZcsYOHBg6TGr1crAgQNZsGBBmX0WLFhw3PUAQ4YMOen1Uj7l+Wz+LScnh8LCQqKiojwVZpVU3s/mueeeo3bt2tx8883eCNPzOlwNtiDaW7fShq28M833o3Ll+Wx+//13evTowd13301sbCxt2rThpZdewm63eyvsKqM8n0/Pnj1ZtmxZ6fTr1q1b+euvvzxaeL9K2zYbDm0hI9/gs5yeACdd6ODrfECJHHDgwAHsdjuxsbHHHY+NjSU1NbXMPqmpqS5dL+VTns/m3x599FHi4+NP+EWTM1Oez2bu3Ll88sknjBs3zhsheke1aGg1HICrbNP4Y9UeNu/z7bNy5flstm7dys8//4zdbuevv/7iqaee4o033uCFF17wRshVSnk+n6uuuornnnuOXr16ERgYSJMmTejXr5+mVj2leJHDd9sjyTJCqVsjlPpRYWVeerJ8ICMjwyvl2ZTISaX2yiuv8P333zNhwgRCQkJ8HU6VlpmZybXXXsu4ceOIjq54K7/OSMmih8AFVDdyeLcCPSvnLIfDQe3atfnoo4/o3Lkzl19+OU888QQffvihr0MTzGd/X3rpJd5//32WL1/OL7/8wsSJE3n++ed9HVrlk7UPNvwJwNcZXQDo0aRWhX3+36WdHSqr6OhobDYbaWlpxx1PS0sjLi6uzD5xcXEuXS/lU57PpsTrr7/OK6+8wtSpU2nXrp0nw6ySXP1stmzZwvbt27ngggtKjzkcDgACAgJITk6mSZOKs3+hS+r3gJhEgvdvYIRtLl+vDOPe/s1oepIVbp5Wnt+bOnXqEBgYiM1mKz3WsmVLUlNTKSgoICgoyKMxVyXl+Xyeeuoprr32Wm655RYA2rZtS3Z2NrfddhtPPPEEVqvGZdxmxVfgKIJ6Xdm8rQ/BnHxaFU6eD0RERBAaGurhYDUiB5h7yHbu3Jlp06aVHnM4HEybNo0ePXqU2adHjx7HXQ8wZcqUk14v5VOezwbg1Vdf5fnnn2fSpEl06dLFG6FWOa5+NomJiaxevZqkpKTS14UXXli60ishIcGb4buXxVI6Knd72CwMw+Dd6b6rK1ee35uzzz6bzZs3lybXABs3bqROnTpK4tysPJ9PTk7OCclaSdJtOL9lupyOww7LvgAgp+11BMWa/7jscYpEzuf5gFeWVPiB77//3ggODjY+//xzY926dcZtt91m1KhRw0hNTTUMw1yBwjGrVufNm2cEBAQYr7/+urF+/XpjzJgxRmBgoLF69Wpf/hiV0uk+m2uvvdZ47LHHSq9/5ZVXjKCgIOPnn3829u7dW/rKzMz01Y9Qabn62fxbpVi1WiLnsGE8H2sYYyKMix97w2j02J/GpjTf/Z1z9bPZuXOnER4ebtxzzz1GcnKy8eeffxq1a9c2XnjhBV/9CJWaq5/PmDFjjPDwcOO7774ztm7dakyePNlo0qSJcdlll/nqR6ickv8xjDERRuEL8cbHv043Gjz6p9H+8V+MFStWGDt2mKtWH3vsMePaa68t7bJ161YjLCzMePjhh43169cbY8eONWw2mzFp0iSvhKxE7hjvvvuuUb9+fSMoKMjo1q2bsXDhwtJzZ5999nGJnGEYxo8//mg0b97cCAoKMlq3bm1MnDjRF2FXCaf6bPr27Wtcf/31pe8bNGhgACe8xowZ4/3AqwBXPpt/q1SJnGEYxq93GcaYCGP+qxcbDR7907j/u+U+DcfVz2b+/PlG9+7djeDgYKNx48bGiy++aBQVFXk56qrDlc+nsLDQeOaZZ4wmTZoYISEhRkJCgnHXXXcZhw8f9n7gldk3lxnGmAjjzSHBRs0BtxkNHv3TiBp8lwGUfh7XX3+90bdv3+O6zZgxw+jQoYMRFBRkNG7c2Pjss8+8FrLFMDQm64yMjAwiIyNJT08nIiLC1+GISEW0exmM64/DFkzn7LdJt0QwZVRfmsT45lk5EXHBkZ3wVjvAgHuWMuSrvSSnZfL+1Z04t20dX0d3UnpGTkTEXeI7QZ32WO35jI5fgcOA9/xwBatIlbTsc8CARn3YH1yf5OIt985qfPLn4yoCJXIiIu5yzKKH4UWTseDgt6TdbN2f5ePAROSUigpg+Zdmu8vNLNx6EICWdSKIqlaxF/sokRMRcac2l0JQOMEZ27i74R6Nyon4gw1/QPZ+qB4Hiecxf4uZyJ2q7EhFoURORMSdgqtD+8sBuDV0JgC/alROpGJbYu7kQKfrwBbIgi0HACVyIiJVU+cbAYjcMZmLm9rMUbkZGpUTqZD2bYAdc8Fihc7Xs/tILtsP5mCzWujWqOLv0a1ETkTE3eLaQEJ3cBTxSOwSAH5dsZttB7J9HJiInKB4X1VanAuR9Zi3yRyNa1s3kvCQQB8G5hwlciIinlC86CFu8w8MaFELh4FPd3sQkTIUZMPK78x28e/szI37AOjTPMZXUblEiZyIiCe0Gg6hNSE9hSea7wbgt6Q9bNeonEjFsfpnyM+Amo2g8TkU2R3MKR6R69dCiZyISNUVGAodrgag8Y4fOadFDHaHwbtawSpSMRgGLP3EbHe5CaxWVqQcITOviBphgbSvV8On4TlLiZyIiKd0vsH8uvEf/tM9DDBXsGpUTqQC2L0c9q4EWzB0vAaAmcnmtGrvZjHYrBZfRuc0JXIiIqfx3XffERoayt69e0uP3XjjjbRr14709PSTd4xuBo36AAatU3+lX/GonFawilQAJaNxrS+CMHN16qyN+wHo5yfPx4ESORGR07riiito3rw5L730EgBjxoxh6tSp/P3330RGRp66c/ED1Cz/ivvPaQjAhBW72XFQo3IiPpNzCNaMN9tdbwZgX2Yea3ZnAP6z0AEgwNcBiIhUdBaLhRdffJFLL72UuLg43n33XebMmUPdunVP37nFeVCtNmSl0jFnIf1axDEzeT/vTd/MayPbez54ETnRyu+gKA9i20K9rgDM2WgucmhTN4KY8GBfRucSjciJiDjh/PPPp1WrVjz33HNMmDCB1q1bO9cxIAg6XWu2l37K/QOaAfCLRuVEfMMwjtaO63qTuUcyMLN0WrW2ryIrFyVyIiJOmDRpEhs2bMButxMbG+ta507XAxbYOoOO1Q7Rt3nxs3JawSrifdtmwcHNEBQObS8DwO4wmLPJTOT6+knZkRJK5ERETmP58uVcdtllfPLJJwwYMICnnnrKtRvUbABNB5rtZZ9z/8Cjo3I7D+a4OVoROaUlxYsc2l9u7o0MrNx1hCM5hUSEBNAxoYbvYisHJXIiIqewfft2zjvvPB5//HGuvPJKnnvuOcaPH8/y5ctdu1HJoocVX9MpPow+JaNyM7Tbg4jXZOyFDRPNdpebSw/PTDZH43o3iyHA5l+pkX9FKyLiRYcOHWLo0KEMHz6cxx57DIDu3bszbNgwHn/8cddu1mwwRNSF3EOw7vejz8ot16iciNcs/xIMO9TvAbGtSg+XlB3p60erVUsokRMROYmoqCg2bNjAhx9+eNzxiRMnMmnSJNduZgsoflYOWPopnRvUpHezaIocBmNVV07E8+xFsOxzs33MaNzBrHxW7ToC+N/zcaBETkTEezpdCxYb7JwP+9bzQPGzcuOX7yLlkEblRDxq49+QuQfCoqHVhaWH52w6gGFAYlw4sREhPgywfJTIiYh4S0Q8tBhmtpd+RucGURqVE/GWkkUOHa+BgKN14kp3c2jhX2VHSiiRExHxppJFDyu/h4Ls0mflfl6mUTkRjzm4BbbOACzQ5cbSww6HwezSRM7/plVBiZyIiHc1PgdqNoT8dFjzC10aalROxONKCgA3G2T+/hVbvTudg9kFVA8OoHODmr6J7QwpkRMR8SarFToXjwgU/89Fo3IiHlSYC0nfmO1jFjnA0WnVs5vWItDPyo6U8M+oRUT8WcdrwBoIe5bDnhV0aRhFr6bmqNz7MzUqJ+JWa3+F3MMQWd8ckTvGzOR9APT1s225jqVETkTE26pFQ6vhZrtkVK54BetPS3ex67BG5UTcZmnxIofO14PVVnr4SE4BSSlHAP99Pg6UyImI+EbX4imeVT9B7mG6Nozi7Ka1ip+V2+Lb2EQqi72rYNcScwS803XHnZqz6QAOA5rHVie+RqiPAjxzSuRERHyhfg+IbQNFubDCfH7n/gHNAfhpaYpG5UTcoWQ0ruUFUP346dOSbbn8cTeHYymRExHxBYsFut1qtpeMA4eDbo2i6NmkVvGzchqVEzkjeRnmiDccHQEv5nAYfl8/roQSORERX2k7EkIi4fB22DwVOLqCVaNyImdo1Q9QmA0xidDg7ONOrdubwYGsfMKCbHRp6J9lR0ookRMR8ZWgatDxWrO9+CMAujeuRc8mtSi0G7w3XStYRcrFMI7u5NDlJnME/Bglo3E9m9QiOMD2795+RYmciIgvdbkJsMDmKWb1eeChwcXPyi3bxbYD2T4MTsRPbZ8L+9dDYBi0u/yE07NKno/z82lVUCInIuJbtZocrW1VPILQuUEU57SIwe4weHvqRh8GJ+KnFv/P/Nr+Cgitcdyp9NxClu08DEA/P1/oAErkRER8r9tt5tcVX0OBOQL30OAWAPy2cg/JqZm+ikzE/xxJgQ0TzXbJ79Yx5m8+gN1h0DimGglRYV4Ozv2UyImI+FqTAVCzkbn/6qofAWhTN5JhbeIwDHhzSrKPAxTxI0s/BcMBDXtD7ZYnnJ62wdzNoZ8f7+ZwLCVyIiK+ZrUeLUWyeJz5oDYwalBzLBb4Z20aq3el+zBAET9RmAfLvzDb3W8/4XSR3cG09WkADGoV683IPEaJnIhIRdDhKvPB7H1rYcd8AJrFhnNRh7oAvD5Zo3Iip7X2F8g5CJEJ0HzYCacXbz/E4ZxCaoYF0tXPy46UUCInIlIRhNaEdpeZ7SXjSg/fP7AZAVYLszbuZ8n2Qz4KTsQPGAYsKl7k0OUmsAWccMnkteZo3ICWsQTYKkcKVDl+ChGRyqBr8fTq+j8gYw8ADWpVY2SXBABe+ycZo3jaVUT+ZdcS2JsEtmDodP0Jpw3DYPLaVACGtI7zcnCeo0RORKSiiGsD9XuCowiWfV56+L4BTQkKsLJ42yHmbj7gu/hEKrLiotq0HQnVap1wevXudPak5xEWZKN3s2gvB+c5SuRERCqSkkUPSz+DogIA6kSGck33BgC8rlE5kRNlpsHaX812ye/Qv/xTPBrXt3kMIYH+vZvDsZTIiYhUJC0vgOpxkL0P1v9eevjOfk0IDbSxclc6U9al+TBAkQpo2WfgKISE7hDfocxL/il+Pq4yTauCEjkRkYrFFli8bRdHp4qAmPBgbjy7IQBvTtmIw6FRORHAHLle+qnZLqMAMMCW/Vls3pdFgNXCOYmVo35cCSVyIiIVTecbwBoIKYtgT1Lp4dv7NCE8JIANqZn8uXqvz8ITqVDW/w5ZaeZIdqvhZV5SMq3ao0ktIkMDvRmdxymRExGpaMJjj/4P6ZhSJJFhgdzWuzEAb03ZSJHd4YvoRCqWkpHrLjeZI9plqKzTqqBETkSkYiqZIlr9M+QcrR93Y69GRFULYuuBbH5ZsdtHwYlUEHuSzJFra6A5kl2G1PQ8VqYcwWKBwZVkN4dj+V0id+jQIa6++moiIiKoUaMGN998M1lZWafs069fPywWy3GvO+64w0sRi4iUQ0I3iGsHRcdsOQRUDw7gzr5NAHh76ibyi+y+ilDE9xYXj1i3HmGOZJdhyjpzWrVjQg1qR4R4KTDv8btE7uqrr2bt2rVMmTKFP//8k9mzZ3PbbWU/3HisW2+9lb1795a+Xn31VS9EKyJSThYLdC/+B+ficWAvLD11bY8GxEYEs/tILj8sSfFRgCI+ln0QVv9ktruduK9qico8rQp+lsitX7+eSZMm8fHHH9O9e3d69erFu+++y/fff8+ePXtO2TcsLIy4uLjSV0RExCmvz8/PJyMj47iXiIhXtbkEqsVAxm5zt4diIYE27unfDIB3p28mt0CjclIFLf8C7PlQpwPU61LmJek5hSzcehBQIlchLFiwgBo1atCly9EPbODAgVitVhYtWnTKvt988w3R0dG0adOG0aNHk5OTc8rrX375ZSIjI0tfCQkJbvkZREScFhgCXW422ws/OO7U5V0SqFczlP2Z+Xy1cLv3YxPxJXvR0ZIj3W83R7DLMG1DGkUOgxax4TSMrubFAL3HrxK51NRUatc+vv5LQEAAUVFRpKamnrTfVVddxddff82MGTMYPXo0X331Fddcc80pv9fo0aNJT08vfaWkaPpCRHygy01gC4Jdi2HX0tLDQQFW7h9gjsp9MHMLmXmFJ7uDSOWT/Bekp0BYLWh98Ukv+6d0b9XKt8ihRIVI5B577LETFiP8+7Vhw4Zy3/+2225jyJAhtG3blquvvpovv/ySCRMmsGXLlpP2CQ4OJiIi4riXiIjXhcdCm0vN9r9G5S7qWJfGMdU4nFPIuDnbfBCciI+U/C50vsEcuS5DboGdWRv3AzC4kk6rQgVJ5B566CHWr19/ylfjxo2Ji4tj3759x/UtKiri0KFDxMU5/yF1794dgM2bN7v15xAR8Yizihc9rPsV0o+WHAmwWXl4cAsAPp6zlf2Z+T4ITsTL9qyAnfPNkiNdy95XFWD2pv3kFTqoWyOU1vGVdzAmwNcBAMTExBATE3Pa63r06MGRI0dYtmwZnTt3BmD69Ok4HI7S5MwZSUlJANSpU6dc8YqIeFWd9tCgF+yYC0s+hoFjSk8NbRNH+4QarEw5wnvTN/Hs8DY+DFTEC0pG49pcDBEn//94ybTq4NaxWE7yDF1lUCFG5JzVsmVLhg4dyq233srixYuZN28e99xzD1dccQXx8fEA7N69m8TERBYvXgzAli1beP7551m2bBnbt2/n999/57rrrqNPnz60a9fOlz+OiIjzzrrT/LrsMyg4uljLYrHw2NBEAL5ZtJMdB7N9EZ2Id2TshTXjzXbJ70QZCu0Opq03Z/Aq62rVEn6VyIG5+jQxMZEBAwZw7rnn0qtXLz766OjG0oWFhSQnJ5euSg0KCmLq1KkMHjyYxMREHnroIS655BL++OOPk30LEZGKp8UwqNEAcg/Dqh+OO9WjSS36No+hyGHwxuSNPgpQxAuWfAyOIqjfE+I7nvSyxdsOkZ5bSFS1ILo2jPJigN5XIaZWXREVFcW333570vMNGzbEMIzS9wkJCcyaNcsboYmIeI7VZhYI/me0ObXU+YbjSi48OjSR2Zv28/vKPdzWpzFt6kb6LlYRTyjMPVpy5BSjcXB0WnVgy9rYrJV3WhX8cERORKTK6ngNBIXDgWTYMv24U63iIxje3nzE5L+Tyr/KX6TCWvUD5B6CGvUh8byTXuZwGEyu5Ls5HEuJnIiIvwiJgE7Xmu2F759w+qHBLQi0WZiz6QDzNh/wcnAiHmQYRxc5dL/DHKE+iVW700nNyKNakI2zm0Z7KUDfUSInIuJPut0GWGDzVNiffNyphKgwru7eAIBX/t6Aw2GUcQMRP7RlOuzfAEHVzZHpUyiZVu3XojYhgSdP+CoLJXIiIv4kqtHRaaVFH55w+p7+TakWZGP17nT+WrPXy8GJeEjJCHTHayHk5M9/GobBn6vMvdeHtqn806qgRE5ExP+UPOid9B3kHDruVHT1YG7r0wSA1/9JptDu8HZ0Iu61P9kcgcYC3W875aXLdx4m5VAu1YJsDGxZebflOpYSORERf9PgbIhrC0W5sPyLE07f0rsR0dWD2H4whx+WaJ9o8XMlz8YlngdRjU956a8rzNG4Ia3jCA2q/NOqoERORMT/WCxw1l1me/E4sBced7pacAD39m8GwNvTNpFTUOTtCEXcI+cQrPzebJ+m5Eih3cHE1ebjBMM71vV0ZBWGEjkREX/U5hKoFgMZu2H97yecvrJbfepHhbE/M59P527zQYAibrDsM3PkOa6dORJ9CnM27edQdgHR1YM4u0ktLwXoe0rkRET8UUAwdL3FbJdMPR0jKMDKQ4ObA/DhrK0cyi7wZnQiZ66owBxxBnME+jT7pZZMq57fLp4AW9VJb6rOTyoiUtl0uQlsQbBrCexcdMLpC9rF0zo+gqz8IsbO2OyDAEXOwJqfIXMvVI+FNhef8tLs/CKmrDOLAI+oQtOqoERORMR/Va8N7S432/PfOeG01Wrh0aGJAHy1YAcph3K8GZ1I+RkGzH/XbHe/wxyBPoXJ61LJLbTTsFYY7etVre3plMiJiPiznveZXzdMhAObTjjdu1k0ZzetRYHdwav/JJ9wXqRC2jwV9q0zCwB3uem0l5dMqw7vUBfLaaZgKxslciIi/iymObQ4FzhmBOMYFouFx89ticUCf6zcw/Kdh70fo4ir5r1tfu18A4TWOOWlB7LymVu8JV1Vm1YFJXIiIv7v7PvNryu/g8y0E063jo/k0k71AHjhz3UYhrbukgpszwrYPgesAactOQLw58o92B0G7etF0ii6mhcCrFiUyImI+Lv6Z0FCd7AXlLltF8B/hrQgNNDG8p1HSmttiVRI84qf92xzCUTWO+3lvyYdnVatipTIiYhUBiWjcks+gfzME07HRoRwe1+zKv5/J20gv8juzehEnHN4O6z71Wz3vPe0l28/kE1SyhGsFji/fR2PhlZRKZETEakMmg+DWs0gPx2WnbhtF8BtfRoTGxFMyqFcvpi/3bvxiThjwftgOKBJf3MbutP4rXg07uym0dQOD/F0dBWSEjkRkcrAaoWzi1ewLnz/hG27AMKCAvjP4BYAvDt9s4oES8WScwhWfGW2S1Zjn4JhGPyWtBuAEVV0WhWUyImIVB7tLjeLp2bshjXjy7zkkk71aFUngsy8It6eutHLAYqcwpJPoDDHHIlr3O+0l6/enc7WA9mEBFoZ0ibO8/FVUErkREQqi4Bgs3gqmOUbylidarVaePK8lgB8vWgnm/dleTNCkbIV5sHi/5ntnvefdjsuOFo7bmDLWKoHB3gyugpNiZyISGXS5SaziOq+dWZR1TL0bBrNwJa1sTsMXvl7vZcDFCnDyu8gez9EJkDrEae93O4w+GOVmchV5WlVUCInIlK5hNYwi6jC0aKqZRh9bksCrBamrt/H/OJiqiI+4XDAgvfM9ll3gS3wtF3mbznA/sx8aoQF0qd5jIcDrNiUyImIVDZn3WUWU90+B3YvK/OSJjHVubp7fQBemLgeu0NFgsVHkv+Cg5shJBI6XedUl5Jp1fPa1iEooGqnMlX7pxcRqYwi60LbkWa7pLhqGe4f2JzwkADW7c3gl+W7vBScyDEMA+a9Zba73gLB1U/bJa/Qzj9rU4GquSXXvymRExGpjEqKqa7/HQ5uKfOSqGpB3Nu/KQCv/ZNMTkGRt6ITMW2bBbuWQEDI0YU6pzF1fRpZ+UXUrRFK5/o1PRxgxadETkSkMoptDc0Gm8VVF4w96WXX92xIQlQo+zLz+Wj2Vi8GKALMft382ul6qF7bqS4l06rDO8RjtZ5+dWtlp0RORKSyKtm2K+kbyNpX5iXBATYeG2qWI/nfrK2kZeR5Kzqp6nYuNJ/jtAYeLWZ9Gvsy85iZbP5d1rSqSYmciEhl1eBsqNsFivKOrgosw7lt4+jcoCa5hXZenZTsxQClSisZjetwFUTWc6rLT0t3UeQw6NygJs1jwz0YnP9QIiciUllZLNDnP2Z78cfmFkhlXmbhqfNbATB++S6W7TjsrQilqtqzAjZPAYsNej3oVBe7w+DbRTsBuKpbfU9G51eUyImIVGbNh5pbHhVmm3uwnkSHhBqM7GyOijzz+1qVIxHPKhmNa3spRDVyrsum/ew+kktkaCDntavjweD8ixI5EZHKzGKBPg+b7UX/g9wjJ730kaGJhAcHsHp3Oj8uTfFOfFL17FsPG/4ELNBrlNPdSkbjLu5Ul5BAm4eC8z9K5EREKrvECyCmJeRnwOKPTnpZTHgwDwxqDpjlSNJzCr0VoVQlc94wv7a6EGonOtVlb3ou09anAZQWshaTEjkRkcrOaj36rNzC9yE/86SXXtejAc1qV+dQdgFvTtHCB3Gzg1tgzXiz3fs/Tnf7YUkKDgO6NYqiaW0tcjiWEjkRkaqg9UVQqynkHoYln5z0skCblWcvbA3AVwt3sH5vhrcilKpg7ptmbcNmQ6BOO6e6FNkd/LDEnOrXaNyJlMiJiFQFVhv0fshsL3gPCnJOemnPptGc2zYOhwFjfl+LYWjhg7jBkRRY+b3Z7uP8aNzM5P3sTc8jqloQQ9vEeSg4/6VETkSkqmg7Emo0gOz9sOzzU176xHmtCAm0snjbIf5Ytdc78UnlNu9tcBRBo76Q0M3pbt8s2gHApZ3rERygRQ7/pkRORKSqsAVC7+JVgvPehsKT7+JQt0Yod/Uz92F9aeJ6svO1D6ucgcxUWP6l2S5ZRe2EXYdzmLlxPwBXqnZcmZTIiYhUJe2vgoi6kJUKK7465aW39WlMQlQoqRl5jJ2x2UsBSqU0/12w50NCd2jYy+luPyxJwTCgZ5NaNIqu5sEA/ZcSORGRqiQgCM5+wGzPfQuKCk56aUigjafOM3d8+HjONrYfyPZ8fFL5ZB+EpZ+a7T4Pm7UNnVBod/B96SKHBp6Kzu8pkRMRqWo6XQvVYyFjF6z87pSXDmoVS5/mMRTYHTz35zovBSiVyqIPoDAH6rSHpgOd7jZtfRr7M/OJrh7EoFaxHgzQvymRExGpagJDoed9Znvum2A/+fNvFouFMRe0ItBmYfqGfUzfkOalIKVSyEs3dxQBs26ck6NxAN8U7+QwsksCQQFKV05GfzIiIlVRlxshrBYc3g6rfzrlpU1iqnPT2eZ+mM/+sY68QrsXApRKYcH75o4iMYmQeL7T3XYezGHOpgNYLHBlVy1yOBUlciIiVVFQNehxj9me8/opR+UA7h3QjNiIYHYczOF9LXwQZ+QcggVjzXa/x8wdRpz07WJzNK53sxjq1wrzRHSVhhI5EZGqqtutEFoTDm6GVT+c8tLqwQE8c4G548MHs7awed/Jt/kSAWDu/0FBJsS1hZbDne5WUOTg52XmIoerVHLktJTIiYhUVcHh0OtBsz3zFSjKP+XlQ9vEMSCxNoV2g8d/WYPDoR0f5CQyU2HxOLPd/ymXRuMmr0vlQFYBtcODGdCytocCrDyUyImIVGVdb4XqcZC+82jB1pOwWCw8O7w1oYE2Fm8/xM/LdnkpSPE7s1+Holyo1w2aDXap6zcLzWnVK7omEGhTmnI6+hMSEanKgsKO7ns5+7VT7sEKUK9mGKMGNQfgxb/WcyDr1KN4UgUd3nF0C7gBT7m0UnXN7nQWbD2IzWrhck2rOkWJnIhIVdfpeqhRH7LSYPFHp738xrMb0qpOBOm5hbw4cb0XAhS/MutVcBSae6o26uNS149mbwXg/HZ1qFsj1BPRVTpK5EREqrqAIOg32mzP/T+z9tepLrdZefnitlgsMGHFbuZuOuCFIMUvHNgEK7812wOedqlryqEcJq7eC5jbw4lzlMiJiAi0uxyiW0DekaMlI06hfUINru/REIAnf12t2nJimvESGA5oPgzqdXGp6ydzt2F3GPRuFk3r+EgPBVj5KJETERGw2qD/E2Z7wVjIPv0o20ODmxMbEcz2gzmMVW05SV0Na38x2yV/l5x0OLuAH4r3VdVonGuUyImIiKnlheZ+mAVZ5hTraYSHBPLshWZtuQ9nbWFTmmrLVWnTXzS/tr7YrB3ngq8X7iC30E6rOhH0ahrtgeAqLyVyIiJisligf/FzTYvHQfru03YZ0jqOgS2La8tNWK3aclVVyhLY+DdYrHDO4y51zSu08/n87QDc3rcxFhdWuYoSOREROVbTAVC/J9jzzXIkp2HWlmtDWJCNJdsP81NxRX6pYqY/b35tfxVEN3Op6/jluziYXUDdGqGc27aOB4Kr3JTIiYjIURaLWfsLYMVXcGjrabvUrRFaWlvupb82sC8zz5MRSkWzbTZsmwXWQOj7iEtd7Q6DccUlR27u1UgFgMtBf2IiInK8Bj2h6UBwFMGMl53qckPPhrSpa9aWe3LCGgxDU6xVgmHAtOfMducboGYDl7pPWZfK9oM5RIYGcnnXBPfHVwUokRMRkRP1Lx6VW/0j7F522ssDbFZeu7Q9AVYLk9el8ceqvR4OUCqENeNh1xIIPGaHECcZhsGHs8zRuGvPakC14ABPRFjpKZETEZETxXeA9lea7UmjzZGX02hZJ4J7+5vPR435bQ37M7V9V6VWmAtTnzHbvR6E8DiXui/ZfpiklCMEBVi5vmdDt4dXVSiRExGRsg142hxpSVl0tD7Yadx1ThNa1YngcE4hT/+2xsMBik8teA/SUyCiHvS4x+Xu/5u1BYBLOtUjJjzY3dFVGUrkRESkbBHx5kgLwJQx5gjMaQTarLw2sh0BVgt/r0lloqZYK6fMVJhTXGtw4DMQFOZS901pmUzbsA+LBW7t3cj98VUhSuREROTketxjjrikp5gjME5oHR/J3ec0BeCp39ZwMEtTrJXOtOehMBvqdYW2l7rc/aPilaqDW8XSOKa6u6OrUvwukXvxxRfp2bMnYWFh1KhRw6k+hmHw9NNPU6dOHUJDQxk4cCCbNm3ybKAiIpVBUBgMetZsz/k/yHBuhO3uc5qSGBfOoewCnv59rQcDFK/bkwRJ35jtIS+bJWtcsP1ANhNWmMWmb+vTxM3BVT1+l8gVFBQwcuRI7rzzTqf7vPrqq7zzzjt8+OGHLFq0iGrVqjFkyBDy8lTrSETktNpcYo68FGYfLTVxGkEBVl4f2R6b1cLEVXv5a7WmWCsFw4B/HgcMaDsSErq6fIs3p2ykyGHQr0UMnRvUdH+MVYzfJXLPPvssDz74IG3bOrePm2EYvPXWWzz55JMMHz6cdu3a8eWXX7Jnzx5+/fXXk/bLz88nIyPjuJeISJVkscDQV8z2ym9h93KnurWpG8nd/cwRl6d+XcMBTbH6v/W/w455EBBqPhvnojW70/l95R4AHh7Sws3BVU1+l8i5atu2baSmpjJw4MDSY5GRkXTv3p0FCxactN/LL79MZGRk6SshQYUKRaQKq9cF2l1utp0sRwJwT/9mJMaFczC7gMfGr1KhYH9WlA+Ti+sL9rwXIuu5fIvX/kkG4ML28bSOj3RndFVWpU/kUlNTAYiNjT3ueGxsbOm5sowePZr09PTSV0qK9g8UkSpuwBhzJCZlIayd4FSXoAArb13RgaAAK1PX7+ObRTs9HKR4zMIP4MgOCK8DZ9/vcvcFWw4ya+N+AqwWHhrc3AMBVk0VIpF77LHHsFgsp3xt2LDBqzEFBwcTERFx3EtEpEqLrAu9HjDbTpYjAUiMi+DRoYkAvDBxHZv3ZXkoQPGYrH0w+3WzPeBpCHZtpalhGLz6j/n/8Su71adBrWrujrDKqhCJ3EMPPcT69etP+WrcuHG57h0XZ1aaTktLO+54Wlpa6TkREXFSz/sgoi6k74QFY53udmPPhvRuFk1eoYMHflhBQZHDg0GK2814EQoyoU4HaHeFy90nr0tjxc4jhAbauHdAU/fHV4VViEQuJiaGxMTEU76CgoLKde9GjRoRFxfHtGnTSo9lZGSwaNEievTo4a4fQUSkaggKg4El5UjeNAvDOsFqtfD6yPbUDAtkze4M3pyy0YNBilulroHlX5rtoa+A1bXUwe4wSp+Nu7lXI2qHh7g7wiqtQiRyrti5cydJSUns3LkTu91OUlISSUlJZGUdHapPTExkwgTz+Q2LxcIDDzzACy+8wO+//87q1au57rrriI+PZ8SIET76KURE/FjbS48pR/K8091iI0J45ZJ2APxv9hYWbDnoqQjFXUrKjRgOaDUCGrg+APLL8l1s3pdFjbBAbutbvtk1OTm/S+SefvppOnbsyJgxY8jKyqJjx4507NiRpUuXll6TnJxMenp66ftHHnmEe++9l9tuu42uXbuSlZXFpEmTCAnRvwpERFxmsZiFYMEsDLtnhdNdh7SO44quCRgGjPoxifScQg8FKW6R/DdsmwW24KOFoV2QV2jnralmAf67+jUhIiTQ3RFWeRZDa8GdkpGRQWRkJOnp6Vr4ICICMP5WWP0j1O8BN/7tdIX/7Pwizn93LtsOZHNeuzq8d2VHLC7uDiBeUJADH/SAw9vNPXfLUTfu4zlbeWHieupEhjDjP/0ICbS5Pcyqzu9G5EREpIIYWFyOZOcCWPG1092qBQfw1uUdCCje9eGX5bs9GKSU26xXzCQuoi70fsjl7pl5hYydsRmABwY2UxLnIUrkRESkfCLrwTmjzfY/Tzi9DytA+4QaPDCwGQBjfl/LzoM5nohQymvvSpj/ntk+7w0IDnf5FuPmbONwTiGNY6pxSSfXiweLc5TIiYhI+Z11N8R3hPx0mPiQ0zs+ANzZryldG9YkK7+Iu79dTl6h3YOBitPsRfD7fWDYzQUOLYa5fIsDWfl8PGcrAA8PbkGATemGp+hPVkREys8WAMPHgjUQkifC2l+c72q18NYVHakZFsjq3ek8+8c6DwYqTlv0IexNgpBIGPZquW7x3vTN5BTYaV8vkqFtVLPVk5TIiYjImYltffQZqr8egWzny4rUrRHK21d0xGKB7xbv5OdluzwUpDjl8Haz+C/AoOchPPaUl5cl5VAO3yzaAcCjQxO1kMXDlMiJiMiZ6/0Q1G4FOQdg0qMude3TPIYHBph7bz4xYTXr92Z4IkI5HcOAP0dBYQ406AWdrivXbV76az2FdoPezaLp2TTazUHKvymRExGRMxcQBBe+BxYrrP4Jkie51P3e/k3p2zyG/CIHd369jIw81ZfzutU/wZZpZs24C95yupzMsaasS+PvNanYrBYeP7el+2OUEyiRExER96jXGc66y2z/+SDkpZ/6+mNYrRbeurwDdWuEsv1gDg//tBKVOfWi7IMw6TGz3edhiG7m8i2y8ot4+rc1ANzWpzEt66jmqjcokRMREfc55wmIagyZe2DK0y51rVktiPev7kSQzco/a9MYV7zqUbxg8pOQc9CcHj/7/nLd4vV/ktmbnkeDWmHcP8D1RFDKR4mciIi4T1AYXPiu2V72OWyb7VL39gk1ePqCVgD8d1Iyi7ZqP1aP2zIDVn4LWOCCd8xpchclpRzhiwXbAXhxRFsV//UiJXIiIuJeDXtBl5vM9u/3QkG2S92v7l6fizrWxe4wuOe7FezLyPNAkAKY23D9+YDZ7nYrJHR1+RaFdgePjV+FYcDFnerSq5kWOHiTEjkREXG/gc9CRD2znMX0F13qarFYePGiNrSIDWd/Zj53fqNiwR4z/QXzMwqPh/5PlesWH8/ZxobUTGqGBfLkea3cG5+clhI5ERFxv5AIc+UjwML3IWWJS93DggL44JpOhIcEsGzHYR7+eRUOhxY/uNWmqbBwrNk+///Mz8xF2w9k89bUjQA8dX4roqq5Pi0rZ0aJnIiIeEazQdDuCsCA3+6GonyXujeOqc7/rulMgNXCHyv38H/FCYO4QdY++PUOs931Vmgx1OVbGIbBE7+uJr/IQa+m0VzUsa6bgxRnKJETERHPGfoyVIuBA8kw+zWXu/dsGs1LF7cF4N3pm/lpaYq7I6x6HA6YcAdk7zdXqQ5+vly3+WX5buZtPkhwgJUXL2qjHRx8RImciIh4TlgUnFucwM39P5enWAEu65LAPec0BWD0L6uZv/mAOyOseha+bxb+DQiBSz+FwFCXb3EwK58XJpp74z4wsDkNalVzd5TiJCVyIiLiWa1GQOuLwFEEP15nTuu5aNSg5lzQPp4ih8EdXy9j875M98dZFexJgqnPmO0hL0Ht8u2+8OLE9RzOKSQxLpxbejdyW3jiOiVyIiLiWZbi+mTRzc1CwT/dCHbXtuCyWi28dmk7OjeoSUZeETd+voQDWa49c1fl5WfBzzeBoxASzz9aIsZFvyXt5pcVu7FY4JVL2hFoUyrhS/rTFxERzwuJgMu/gaBw2DEXpoxx/RaBNj66tjP1o8JIOZTLrV8uVVkSV/z9KBzaAhF1zaLN5XimbVNaJqN/WQ3APec0pUNCDTcHKa5SIiciIt4R0xwu+sBsLxwLq392+Ra1qgfz2Y1diQwNZMXOIzz040qVJXHG6p8h6WuwWOHij8xnF12UnV/End8sJ6fAztlNa/HAwOYeCFRcpURORES8p+UF0GuU2f7tHkhd4/ItmsRU58NrOhNoszBx9V5em5zs5iArmcPb4c8HzXbv/5g7b7jIMAxG/7KazfuyiI0I5u0rOmKzapVqRaBETkREvKv/k9D4HCjKhR+ugdzDLt+iR5NavHJxOwA+mLmFcbO3ujvKysFeCONvgfwMSOgOfR8t122+XriD31fuwWa1MPaqTkRXD3ZzoFJeSuRERMS7rDaz7EVkfTi8DX65zaxt5qJLOtfjoUHm9N6Lf63n07nb3B2p/5v6DOxaAsGRcPE4sAW4fIuklCM896dZamT0sES6NHR9WlY8R4mciIh4X1gUXP6VWcts02SY9d9y3eae/k25t79ZY+65P9fx5YLtbgzSzy39FBa8Z7YvfAdqNnD5FoezC7j7m+UU2g2GtI7l5l4qNVLRKJETERHfiO9g7vEJMOsVSJ7k8i0sFgujBjXnzn5NAHj6t7V8vXCHG4P0U5unwsT/mO1znoDWI1y+hcNhMOrHJHYfyaVBrTBeG9leuzdUQErkRETEdzpcZe71CeYU68EtLt/CYrHwyJAW3NanMQBP/rqG7xfvdGeU/iVtHfx4Axh2aH8l9Hm4XLf5YNYWZiTvJzjAyvtXdyIiJNC9cYpbKJETERHfGvKS+SB+frq5+KEg2+VbWCwWRg9L5Kazzam/0RNWV819WTPT4NvLoCATGvQyCzGXYxRt3uYDvFG8Gvj54W1oHR/p7kjFTZTIiYiIbwUEwcgvoHos7FsHv98Lhuu14SwWC0+d35LrezTAMOCR8auYsGKXBwKuoApy4LvLIT0FajUtfgYxyOXbbN6Xxb3frcBhwMjO9bisa4IHghV3USInIiK+F1HHTOasAbBmvLmxezlYLBaeubA115xVH8OAh35cyS/Lq0Ay53DAL7fCnhUQGgVX/1Suor8ph3K45uNFHMouoG3dSJ4b3sYDwYo7KZETEZGKoUEPc5oVYPJTsGlquW5jsVh47sI2XNktAYcBo35cydgZmzHKMcrnN6Y+DRv+BFsQXPEtRDV2+Rap6Xlc/fEiUjPyaFa7Ol/c1I3QIJsHghV3UiInIiIVR7fboN0V5oP6319ZrpWsAFarhRdHtOXW3uYzc6/9k8zoX1ZTaHe9Xl2Ft/RTmP+u2R7xgZkQu+hgVj5Xf7yQnYdyaFArjK9v6U5UNdenZcX7lMiJiEjFYbGYG7q3vADsBfDD1bDut3Ldymq18MR5rXhueGusFvh+SQo3f7GUzLxCNwftQ/8uM9L2UpdvkZ5byLWfLGbL/mziI0P45pbuxEaEuDlQ8RQlciIiUrEEBMGln0ObS8FRBD/daG76Xk7X9WjIR9d2ITTQxuyN+xn54QL2pue6L15f2bnojMuMZOcXccNni1m3N4Po6sF8fUt36tUMc3+s4jFK5EREpOKxBcDFH0GHq81EZfwtsOKbct9uYKtYfry9BzHhwWxIzeSisfNZtyfDjQF72dZZ8NVFZpmRhr3LVWYkr9DOLV8sZcXOI0SGBvL1Ld1oHFPdQwGLpyiRExGRislqgwvfg843AAb8dhcs/azct2tbL5IJd/WkWe3qpGbkMfLD+cxM3ue2cL1m0xSzVlxhNjTpD1f96HKZkez8Im7/ahkLth6kenAAX97UjcS4CA8FLJ6kRE5ERCouqxXOfwu632G+//MBWPhhuW9Xr2YYP9/Zkx6Na5FdYOemz5fwzrRN2B1+sqJ13e/w3ZVQlActzoUrv4cg16ZC0zLyuOx/C5i1cT8hgVY+vaEr7RNqeCZe8TglciIiUrFZLDD0Feh5n/l+0qMw7+1y3y4yNJAvburG5V3M8iRvTtnIdZ8uYl9mnpsC9pBVP8JPN4CjEFpfDJd9CQHBLt1iQ2oGF42dx9o9GdSqFsS3t55Ft0au15uTisNiVOrCOu6TkZFBZGQk6enpRERo+FlExOsMA2a8BLNfNd+f8wT0feSMbjl+2S6e/HUNuYV2oqsH8/YVHTi7abQbgnWzZZ/DHw8ABnS4Bi58x5x6dsHsjfu565vlZOUX0SSmGp/d0I36tbSwwd8pkXOSEjkRkQpi1msw4wWz3fs/0P/Jcu0nWmLzvkzu/mYFyWmZWCxwS69GjBrUomIUwzUMs0bclKfM911vhWGvmlPOTnI4DD6as5XX/knG7jA4q3EU/7umC5FhgR4KWrxJiZyTlMiJiFQg8945mtz0uAcGv3BGyVxugZ1n/1jL90tSAGhYK4xXLmnHWY1ruSPa8snLgN/vOVpHr+d9MOg5l37O/Zn5jPoxiTmbDgBwcae6vHJxO4IC9GRVZaFEzklK5EREKphFH8HfxbXTWl4Iw9+DkMgzuuX0DWk8/ssaUjPM5+Wu7l6fR4clEhHi5dGr1DXw43VwaIu5/+zgF6H77S4lcbM37mfUjys5kJVPSKCVZy9szWVdErCcQcIrFY8SOScpkRMRqYCWfwV/PmguAIhqDCO/gDrtzuiWGXmFvPzXBr5bvBOAWtWCeGhwCy7vmoDN6oUkaMU3MHGUuTI1oh6M/BwSujrdfX9mPi/9tZ4JK3YD0CI2nPeu6kiz2HAPBSy+pETOSUrkREQqqF1LzdWc6SlgC4ZzX4VO15/RVCvA/C0HeHLCGrYeyAYgMS6cx4Yl0rd5jGdGtQpz4a//wIqvzfdNBsDF46Cac9O7dofBt4t38tqkDWTkFWGxwHVnNWD0uS0JCawAz/uJRyiRc5ISORGRCiznEPx6J2ycZL5vPgzOex0i653RbQvtDr5asIO3p20iPdfco7V9vUju6d+MgS1ruy+hO7jFnEpNWwMWK/R7HHo/5NSiBsMwmJm8nzenbGT17nQA2tSN4MURbVUfrgpQIuckJXIiIhWcwwHz34HpL5hTrUHVzRWt3W5zuVTHvx3OLmDsjM18vWgHeYUOAFrWieCmsxtyXrs6hAUFlO/GRflmzLNfN6dSq8XAJR9D436n7VqSwL01dSMrd5kJXHhwAA8Nbs61PRp6ZxpYfE6JnJOUyImI+Il9G+CP+yFlofk+vhNc8PYZPzsHcCArn4/nbOOrBdvJLrADZvJ0YYd4ruhan7b1XFhssWWGOZV6cLP5vlEfuOh/EBF/ym6Hsgv4PWk3Xy3cwZb95rRvSKCV63o05LY+jYmu7lqRYPFvSuScpERORMSPOByw/HOY8gzkp5vTle2vhH6PQY36Z3z7w9kFfLt4Jz8sSWHnoZzS442jq9GvRW3OSYyhW6MoggPKGAlMXWOOGm7823xfrTYMeQnaXnrS5/r2ZeYxM3k/f6zcw/wtB0u3FKsWZOOq7vW5vW8TJXBVlBI5JymRExHxQ5mpMGk0rP3FfG8NhPaXw9kPQHSzM769w2GwcOtBvl+SwqQ1qRTYHaXnwoJsdKpfk9Z1I2hTJ4KOrKfO+s+wJU8EDDO57HKzOf0bWgMwp0sz8orYdiCbDXszWLMnnYVbD7F5X9Zx37dN3Qgu65LARR3rEu7t0ihSoSiRc5ISORERP7ZrGUx7BrbNLj5ggcZ9oeO1kHg+BIac8bfIyCtk3qYDzEjex4zk/ezPzKcauQy1LuGGgEm0tW4vvXZ6QC9+qH4Nh0IaUOQwKChykJ1fRFpGPrmF9hPubbFAqzoRDGsTx/nt4mkYXe2M45XKQYmck5TIiYhUAimLYe5bkDzx6LGQGtBqOLQYZj6nFnSGSVLuYRybp5O17CfCdk4nwJEPQJ4RyC/23nxmH8om49SraaOrB5MYF05iXDhdGkZxVuMoaoQFnVlcUikpkXOSEjkRkUrk8HZI+tYsvpux6+hxawDEtoF6XaFuJ7PIcI0GUL32iStf7YXm1O2RnZC2FlJXwd6VkLoaOOZ/rVGNocPVGJ1vJMMawZ4juWTmFZFdUERugZ0Aq4WgACthQQHERgQTGxGium/iNCVyTlIiJyJSCTns5nRr8l+QPAnSd5782oBQc7TOsJtlQwpzTn5tdHNocS60uRji2p1xcWKRk1Ei5yQlciIilZxhQPou2LXE3C0idRUc3mGO2BmOsvtYAyGiDtRuZY7kxbWBhO6nLSEi4i5K5JykRE5EpIqyF0JeBhRkQkG2Of0aEGwWHA6Ncmr3BRFPKWcpahERkSrCFmjud+rknqci3qR/RoiIiIj4KSVyIiIiIn5KiZyIiIiIn1IiJyIiIuKnlMiJiIiI+CklciIiIiJ+yu8SuRdffJGePXsSFhZGjRo1nOpzww03YLFYjnsNHTrUs4GKiIiIeJjf1ZErKChg5MiR9OjRg08++cTpfkOHDuWzzz4rfR8cHOyJ8ERERES8xu8SuWeffRaAzz//3KV+wcHBxMXFeSAiEREREd/wu6nV8po5cya1a9emRYsW3HnnnRw8ePCU1+fn55ORkXHcS0RERKQiqRKJ3NChQ/nyyy+ZNm0a//3vf5k1axbDhg3DbreftM/LL79MZGRk6SshIcGLEYuIiIicnsUwDMPXQTz22GP897//PeU169evJzExsfT9559/zgMPPMCRI0dc/n5bt26lSZMmTJ06lQEDBpR5TX5+Pvn5+aXvMzIySEhIID09nYiICJe/p4iIiIi7VYhn5B566CFuuOGGU17TuHFjt32/xo0bEx0dzebNm0+ayAUHB2tBhIiIiFRoFSKRi4mJISYmxmvfb9euXRw8eJA6dep47XuKiIiIuJvfPSO3c+dOkpKS2LlzJ3a7naSkJJKSksjKyiq9JjExkQkTJgCQlZXFww8/zMKFC9m+fTvTpk1j+PDhNG3alCFDhvjqxxARERE5YxViRM4VTz/9NF988UXp+44dOwIwY8YM+vXrB0BycjLp6ekA2Gw2Vq1axRdffMGRI0eIj49n8ODBPP/885o6FREREb9WIRY7+IOMjAwiIyO12EFEREQqDL+bWhURERERkxI5ERERET+lqVUnGYZBZmYm4eHhWCwWX4cjIiIiokRORERExF9palVERETETymRExEREfFTSuRERERE/JQSORERERE/pURORERExE8pkRMRERHxU0rkRERERPzU/wMRkmYt+yMFigAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x22ffc880990>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_2 = y.subs([(c0,c_sols_2 [0][0]), (c1,c_sols_2 [0][1]), (c2,c_sols_2 [0][2])])# 第一激发态试探解\n",
    "y_ex_2 = sqrt(2) *sin(2*pi* x) # 第一激发态精确解\n",
    "plot(y_2,y_ex_2,(x,0,1)) # ,legend=True"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "13120c2f-2c4c-4c9f-a458-092f4e64d535",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x22ffa6eac90>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_3 = y.subs([(c0,c_sols_3 [0][0]), (c1,c_sols_3 [0][1]), (c2,c_sols_3 [0][2])]) # 第二激发态试探解\n",
    "y_ex_3 = sqrt(2) *sin(3*pi* x) # 第二激发态精确解\n",
    "plot(y_3, y_ex_3, (x,0,1)) # ,legend=Truev"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "c5ed5b50-676c-4946-ad6c-5c4e0d3bf841",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 102.130250378683$"
      ],
      "text/plain": [
       "102.130250378683"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N(sol_lamd[2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "fcfa79e3-0169-4bee-96ff-45ad12375e64",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle -28.6462005494646$"
      ],
      "text/plain": [
       "-28.6462005494646"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N(c_sols_3[0][0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "3d26fe62-b3c5-4d18-af81-3d127fc58f6e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle -13.3037104471$"
      ],
      "text/plain": [
       "-13.3037104471000"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N((3*3.14159)**2)-102.13\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "e8ee0ab3-e904-4325-87bf-0ec5efbe66c2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 350x262.5 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scienceplots # 导入'science'画图模块\n",
    "plt.style.use('science') # 采用'science'画图模块\n",
    "fig, ax = plt.subplots() # 建立画布\n",
    "x = np.linspace(0,1,100) # x轴点数\n",
    "c0 = -4.40\n",
    "c1 = -4.99\n",
    "c2 = 4.99\n",
    "y1 = x*(x-1)*(c0+c1*x+c2*x**2) # 近似解\n",
    "y2 = np.sqrt(2) *np.sin(np.pi* x) # 精确解\n",
    "ax.plot(x,y1,linewidth = '0.7',label=r'Approximate solution',color = 'k',linestyle='--') \n",
    "ax.plot(x,y2,linewidth = '0.7',label=r'Exact solution',color = 'k') \n",
    "ax.set_xlabel('$x$') # 设置横坐标名称\n",
    "ax.set_ylabel('$y(x)$') # 设置总坐标名称\n",
    "ax.spines['right'].set_visible(False) # 不显示右边框\n",
    "ax.spines['top'].set_visible(False) # 不显示上边框\n",
    "ax.legend() # 显示标签\n",
    "visible_ticks = { # 设定参数以不显示上和右刻度\n",
    "   \"top\": False,\n",
    "   \"right\": False\n",
    "}\n",
    "ax.tick_params(axis=\"both\", which=\"both\", **visible_ticks) # 去处上和右刻度\n",
    "fig.savefig('Ritz_fig2.png',dpi=600) # 保存图片\n",
    "plt.show() "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6f9d9d9f-8adc-4799-a59a-427b20978ab6",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
